5

(b) Write down an integral which exactly computes the probability you gave in (a). Esti- mate this probability by interpreting the integral as an area and approxima...

Question

(b) Write down an integral which exactly computes the probability you gave in (a). Esti- mate this probability by interpreting the integral as an area and approximating this arca using trapezoid_

(b) Write down an integral which exactly computes the probability you gave in (a). Esti- mate this probability by interpreting the integral as an area and approximating this arca using trapezoid_



Answers

(a) Use a graph of the integrand to make a rough estimate of the integral. Explain your reasoning. (b) Use a computer or calculator to find the value of the definite integral. $$\int_{1}^{2} x^{x} d x$$

Formula 105 saying that they were integral off new. Do you have any by the square, remember? And plus you. Then we get any coaching that two out of three peat square, then times with being humanist to a times with the square with I just be new place SC in a question were given nurse into girl off. Uh, thanks. The extra reviving by this squared on the two minus X. So you always see that we have, uh, number Julia coaches. I didn't comport minus one here. So money is when I go to be and form a formula, we get ego Judah to longer be job with three times p square will be minus one square. Now we're minus B ri minus one minus X minus two In terms am beat you square tongue with humanist. Thanks. Classic constancy. So and we certainly find we see Uganda Jill, arm a tree this one again don't minus X minus four square or the ritual minus expenses. Constancy

Okay, so we have here. Excuse the eggs with its in the girl Vulgar and zero. The one. And we are required to get using a the gap of the integral and and be using a calculator or so for leather. A Now we need to draft first into grand. So I'm just going to insert here. The graph off. Why is a good excuse? Okay, so I grew up with looks something like this. And by using the graph of the indignant to make a rough estimate of the integral we have here, the Range X is equal to zero and X is equal one. So this is our range. So by using the left and right hand three months, psalms, we have, we have not. The eggs is equal 2.5. And is it with one over that the X is equal to With that we have ever zero is equal to zero f A 0.5 is equal to 0.1 toe five and that one is equal to one. So they get that over. Some will make us all this which is I is equipped. The 0.5 times f zero plus 0.5. So we'll have 0.5 they zero plus 0.15 which is equal to 0.6 to 5 for the right hand or the upper. Some we have I is equal to the 0.5 times a 0.5 plus off one which is equal the 0.5 times, um, zero point 15 less one which is approximately equal to 0.56 to 5. So getting the average of little values, we have 0.56 to 5 plus 0.605 over to, and we'll have 0.31 who fight. Okay, so this is our value. Based on the graph of the immigrant. Now we make use of our calculator for so we can write this ass. I is equipped. The integral off excuse the X from zero. The one is just equal to extract. Afford over for integrated from 0 to 1. And we have one recent for over four minus zero is equal to 1/4 or equal the 00.25. So this is our value. Based on a wire. Calgary

This question were people were called under former 0.3 were into ground up about Thanks. You union temps co sign off the you you can buy from the again ever square Best be square times that they go sight off the preview Big him sign on U S A constant c in a question were given in the ground looking about six times That goes to next. There will think of you here we can identify Didn't be one So this would be in the eye and being here we go to the two from my formula We get to go to the feeling our acts They running by ace grab SV Square So have one scrambling to square it Could you find No, we have no go side off to act plus du temps Qusai under two X equals a constant C

Okay, so we have here spirit off X, the X, with its integral foundering 0 to 1. And we are required to get I using a grapple, think ignorant and be using a calculator or so for our solution. We need to get first the graph off. Why is it called the spirit of X two? Have, um, therapist the meat off the value of the grand. I'm just gonna insert here the graph. Okay, so our graph would look something like this. Sorry. You should look something like this. And, ah, where boundary is from zero. The one. So this is all were boundary. So using the left and right, right hand Three months since we have peace for leather e, we have that X is equal to one and end is equal to three minus zero over death off X is equal to three. Now we have apple. Zero is equal to zero f one in sick with one f off to physical. To spirit off to an F three is equal to spirit off three So getting the value off the lower some or the left hand we have I is a local one. Time's up of zero plus f off. One less step off to is you got the one time zero plus one Let's squared off to. So this is approximately equal to 2.414 Next to get the upper some and we'll have I is a good one. Time's up, up one last effort to less effort. Three. And we'll have one times one last period off door, the spirit off three. So we'll have 4.14 So getting the average of both values we have I music with the four point 14 plus 2.414 overthrow is equal to three point when it So this is nobody off our I, um, using that left and right hand Riemann sums. Now I get its value using our calculation in the hour calculate or so For letter B, we have I is equal to zero. The three off. Scare it off. XB X, This is Jessica, while X rays one point 5/1 1.0.5 from 0 to 3. So substituting days, we have three days to 1.5 over 1.5 my nose hoops. My No. Zero is approximately equal the 3.46 fight. So this is our final answer


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