5

Consider the given function and the given interval: f(x) = 14 sin(x) - 7 sin( 2x) , [6 , J] (a) Find the average value fave of f on the given interval.28fave(b) Fin...

Question

Consider the given function and the given interval: f(x) = 14 sin(x) - 7 sin( 2x) , [6 , J] (a) Find the average value fave of f on the given interval.28fave(b) Find such that fave f(c). (Round your answers to three decimal places: ) 1,571 (smaller value) 39.540 (larger value)

Consider the given function and the given interval: f(x) = 14 sin(x) - 7 sin( 2x) , [6 , J] (a) Find the average value fave of f on the given interval. 28 fave (b) Find such that fave f(c). (Round your answers to three decimal places: ) 1,571 (smaller value) 39.540 (larger value)



Answers

Find all values of $x^{*}$ in the stated interval that satisfy Equation (7) in the Mean-Value Theorem for Integrals $(7.6 .2),$ and explain what these numbers represent. (a) $f(x)=\sin x ;[-\pi, \pi]$ (b) $f(x)=1 / x^{2} ;[1,3]$

Do you want? The average volume interval by my link of the animal, the integral of function. I'm not in your vault. The fundamental Go there and talk to this parking. So we end up with still there minus zero. My spawn minus negative one. So in that were too over. Right? With what?

The same. They wanted to get the average value of consigning Rex, and they'll have us work on the interval from zero to pi over two. So compute the length divided by that, and we're gonna give you the but the integral from zero to pi over two. No sign of X t. X. So let's see the coalition in front. Just do over by. But we'll get might see negative coastline of X pi over two and at zero. So let's see. We have to over pine and then pi over two was just zero will have zero and then we'll subtract Negative cosigner one. So subtract a negative one. So that kind of let's become positive and we end up with two over pipe is the average rally of our function on that interval.

In this question we have to find the great value for the function that is a fact sees it was too sign square accent two parsecs and limits we have to use or I can say that the interval we have to use this 02 by by two. So the formula to find the average value is I can say that one divide by b minus A A to B. Integration limits of the function affects so I'm going to substitute here. All the values I got here one divide by five by two minus zero. Limits of integration are 0 to 5 by two and the sinus square X for 68 years. Okay, now to integrate this function we have to make a substitution let you is sign next. So I get to deal with because to cause expertise. Okay we can see that I get here to divide by pi and for 60 X is replaced by do you sinuses replaced by you. So I got your use words Now we cannot use the whole limits because the whole limits stands for X variable and we have to find for you variable. You can see here you is Synnex. So when X zero we got to use zero and when excess bye bye to get signed by by two, that is one. So I can say that the new limits of the integration are 0 to 1 and now use words. Integration is very easy. That is UQ by three. And in this integration we have to substitute the limits. So first of all, I'm going to put here by sorry one. So I got here one by three. And when I put zero I got here zero. So I can say that the answer for this question is You will divide by three by Okay, this is the answer here. Thank you.

So we're trying to find the average value of this function over the interval from zero to pi over two. So we're gonna be using this formula I have written down which is, the average value is equal to one divided by b minus A times the integral from A to B. Of our function F. Of X. So let's go ahead and plug in the values for being A. In our case B is equal to pi over two and A is equal to zero. So we have one divided by pi over two minus zero times the integral from zero to pi over two of X plus co Synnex times dx and so one divided by pi over two. That's the same as two divided by pi. And so we have two divided by pi times the integral from zero to pi over two of X plus cosine X. So now we just need to find the value of this definite integral. And so that's going to be equal to the integral of X, which is X squared divided by two. I add one to the power and then divide by the resulting power and then the integral of cosine, X is equal to sin X. So it's going to be X squared divided by two plus Synnex. And I just used anti differentiation to find these two integral. And so now we're looking from zero to pi over two. So when X is equal to pi over two, we're gonna get pi over two square divided by two plus Sine of pi over two and sine of pi over two is equal to one. So this is going to be equal to two divided by pi times and princes hi squared And then it's going to be divided by four and divided by two. So that's the same as divided by eight. And then we have plus sine of Pi over two which is equal to one. And then we have minus. Um When X is equal to zero, X squared divided by two is equal to zero and sin X is equal to zero, so it's really just minus zero. And so this is going to be equal to two, divided by pi. Times the princes pi squared, divided by eight plus one, Which simplifies to two pi divided, they eat Plus two, divided by Pi.


Similar Solved Questions

5 answers
Use the method of Laplace transforms to solve the initial value problem for the solution y(t) satisfying y" _ 4y' + Ty = et , y(0) = 0,y (0) = 0. Show all your working; including the partial fraction calculations and the other details of the Laplace inversion step.
Use the method of Laplace transforms to solve the initial value problem for the solution y(t) satisfying y" _ 4y' + Ty = et , y(0) = 0,y (0) = 0. Show all your working; including the partial fraction calculations and the other details of the Laplace inversion step....
5 answers
E 5 9 Finiove p 'tpoifol B? H and position vectors 241 larger to best position stccpocscots shoe s 2443 smaller carrd Yecitoa] 5 from the
E 5 9 Finiove p 'tpoifol B? H and position vectors 241 larger to best position stccpocscots shoe s 2443 smaller carrd Yecitoa] 5 from the...
5 answers
[email protected];ONH; 9NHz1. Brz; PBr , [.NaOEt 2.ILO 2. Butyl iodide 3.Excess NI; FNICIHCN Heat DL.CH,MgBr 2 NaCN Ea) In a basic solution at pH of about 12,the predominant form of the amino acid shown above is [ Selectb) Starting from 3-methylbutanone; the set of reagents necessary to synthesize compound B is Select ]
OH @NH; ONH; 9 NHz 1. Brz; PBr , [.NaOEt 2.ILO 2. Butyl iodide 3.Excess NI; F NICIHCN Heat D L.CH,MgBr 2 NaCN E a) In a basic solution at pH of about 12,the predominant form of the amino acid shown above is [ Select b) Starting from 3-methylbutanone; the set of reagents necessary to synthesize compo...
5 answers
Statement-1 : 'lhe position velocity-curve of a particle is always a parabola. Statement-2: For a constant value of $v frac{d v}{d x}$, the position-velocity curve is parabola.
Statement-1 : 'lhe position velocity-curve of a particle is always a parabola. Statement-2: For a constant value of $v frac{d v}{d x}$, the position-velocity curve is parabola....
5 answers
10412. Indicate the formal charge on cach atom in the following structure. SHOW YOUR CALCULATION or points will be given!! ! (4 points @ 0.5 ptslatom)ZHN
104 12. Indicate the formal charge on cach atom in the following structure. SHOW YOUR CALCULATION or points will be given!! ! (4 points @ 0.5 ptslatom) ZHN...
5 answers
(5 points) sample includes 106 body temperatures with mean of 98.20PF Assume that 0 is known t0 be 0.629F. Consider hypothesis test that uses a 0.05 significance level to test the claim that the mean body temperature of the population is 98.69F What is the test statistic? What is the critical value? What is the p-value? What is the conclusion about the null hypothesis (reject or fail t0 reject)? What is thc final conclusion in nontechnical terms?
(5 points) sample includes 106 body temperatures with mean of 98.20PF Assume that 0 is known t0 be 0.629F. Consider hypothesis test that uses a 0.05 significance level to test the claim that the mean body temperature of the population is 98.69F What is the test statistic? What is the critical value?...
5 answers
W 2 2 8 1 I/' 1 ! | 1 1! 1 1 1 [
W 2 2 8 1 I/' 1 ! | 1 1 ! 1 1 1 [...
4 answers
An aqueous solution contains 0.26 M hydrocyanic acid. One Liter ofthis solution could be converted into a buffer by the addition of: (Assume that the volume remains constant as cach substance is added; ) 0.129 mol KOH 00.13 mol HCIO4 00.27 mol KCN 00.27 mol HCIO4 0.26 mol KBr
An aqueous solution contains 0.26 M hydrocyanic acid. One Liter ofthis solution could be converted into a buffer by the addition of: (Assume that the volume remains constant as cach substance is added; ) 0.129 mol KOH 00.13 mol HCIO4 00.27 mol KCN 00.27 mol HCIO4 0.26 mol KBr...
5 answers
Part 2 of 5Divide the numerator and denominator of the function f(x)by 14 to put it In14 +the form of geometrlc serlesPart 3 of 5Here , f(x) has been expressed as the sum on an infinite geometric series withand r = ~(x - 4)_ 14 14Therefore, the power serles for the functlon f(x) can be written as the sum of the Infinite geometric series_=3x3x + 2E# 14" 14 n =(-3)(x-4)"14"+ 1 14n =XSubmit Skip (you cannot come back)
Part 2 of 5 Divide the numerator and denominator of the function f(x) by 14 to put it In 14 + the form of geometrlc serles Part 3 of 5 Here , f(x) has been expressed as the sum on an infinite geometric series with and r = ~(x - 4)_ 14 14 Therefore, the power serles for the functlon f(x) can be writt...
5 answers
The decomposition of PCl 5 (g) to form PCl 3 and Cl 2 has Kc =33.3 at a high temperature. If the initial concentration ofPCl 5 is 0.1000M, what are the equilibrium concentrations of thereactants and products?
The decomposition of PCl 5 (g) to form PCl 3 and Cl 2 has Kc = 33.3 at a high temperature. If the initial concentration of PCl 5 is 0.1000M, what are the equilibrium concentrations of the reactants and products?...
1 answers
Determine from its graph if the function is one-to-one. $$f(x)=\left\{\begin{array}{ll}{3-x,} & {x<0} \\ {3,} & {x \geq 0}\end{array}\right.$$
Determine from its graph if the function is one-to-one. $$f(x)=\left\{\begin{array}{ll}{3-x,} & {x<0} \\ {3,} & {x \geq 0}\end{array}\right.$$...
5 answers
Homework: section 16.1 Score: 16.1.70t 9 I0 complete)-HY Score: 09,Questlon HelpDeterino the graph coresponding the glvem vector equalion. r(u) = (?-)it41k -1sts1Choose the corredi graph thal conesponds Ihe given voctor equatonClick lo select your answror and Ihon click Check Answer
Homework: section 16.1 Score: 16.1.7 0t 9 I0 complete)- HY Score: 09, Questlon Help Deterino the graph coresponding the glvem vector equalion. r(u) = (?-)it41k -1sts1 Choose the corredi graph thal conesponds Ihe given voctor equaton Click lo select your answror and Ihon click Check Answer...
5 answers
19.2.7A sawtooth wave is given byf()=x SI <X <n.Show that(~Iy+I f() =2) sin nx _
19.2.7 A sawtooth wave is given by f()=x SI <X <n. Show that (~Iy+I f() =2) sin nx _...
5 answers
1 1 eolution t0 arguments of functions equation if possible parentneses For Glvcna example , 1 Sin (2x) 1 form and in decimal 30 tan (2x 1
1 1 eolution t0 arguments of functions equation if possible parentneses For Glvcna example , 1 Sin (2x) 1 form and in decimal 30 tan (2x 1...
5 answers
Population and Age Is the size of the population by age related to the state that it's in? Use a = 0.01. (Population values are in thousands:)Under 5 48 2965-17 143 82718-24 57 44025-44 204 128945-64 140 101665 + 36 580AlaskaAlabamaSend data to Excel
Population and Age Is the size of the population by age related to the state that it's in? Use a = 0.01. (Population values are in thousands:) Under 5 48 296 5-17 143 827 18-24 57 440 25-44 204 1289 45-64 140 1016 65 + 36 580 Alaska Alabama Send data to Excel...

-- 0.024207--