5

Given["w) dx # 15 and [" 9x) &x = 4 evaluate the following; (a) [t) glx)] &x(5) f t) g(x)] dx[2f*) - 3g(x)i dxMizix) d*...

Question

Given["w) dx # 15 and [" 9x) &x = 4 evaluate the following; (a) [t) glx)] &x(5) f t) g(x)] dx[2f*) - 3g(x)i dxMizix) d*

Given ["w) dx # 15 and [" 9x) &x = 4 evaluate the following; (a) [t) glx)] &x (5) f t) g(x)] dx [2f*) - 3g(x)i dx Mizix) d*



Answers

Find $F$ as a function of $x$ and evaluate it at $x=2, x=5,$ and $x=8 .$
$$F(x)=\int_{2}^{x}-\frac{2}{t^{3}} d t$$

Section seven No. One problem 24. So we see a definite interval. 4 to 9 of this expression with rational exponents best needed. Let's just try to simplify the expression before we do the immigration. So this is going to be the integral from 4 to 9, and we can write. This is X to the five halves. Minus three. Have minus X to the 1/2 minus three halves DX. So this is the integral from 4 to 9 of X to the five ministry. That's to have. So that's X that the two has is extra the first power minus and they won half minus three. Have a minus two have sex with a minus one DX. So much simpler thing to integrate now. And so if we perform this integration, we get X squared over two minus natural log absolute value of X, and then this needs to be evaluated from four to nine. So calculus is over, and now it's arithmetic. So this is substrate value of nine. You subsidy the value of 99 squared 81 to get 81 over to minus the natural log of nine. We stepped to the fore you get four square. That 16 over to that is eight. So eight minus the natural log of four. So what you have here is 81 halves, minus eight minus and natural agua nine plus the natural order of four. And so this becomes 81 minus 16. There were two you could write. This is natural log of 4/9 just using properties of logarithms. And so this turns into 65/2, plus the natural log of four nights.

Yes. Soon we have been given half off taxes. Goto teaches in zero to x 40 minutes. Seven Uh huh. Mhm or three minus seven. Duty. This will be a quarter integration or tea. 15 X minus two. Address in zero. Collects seven. Duty is good for he. Square by two. Zero to X minus seven X zero Quix. This is a good toe. Extra square minus zero square This seven X minus Cyril two X squared in the seven X. This is a perfect Yeah, in the question we have been asked to find out off except Mexico to five and eight F off to is equal. Two into two square when seven in tow to Is it called egg? Yes. 14. Is he cool? Yeah. Minus six. Yeah. Mhm. Mhm. Uh huh. And half off. Except acceptable five with a 45 This is called Toe Have square. That's 75. This is a culture of contemporary P then is 35. This is a blue bean and I for eight. Go and do it. Square on a seven and wait. This is a guru on 28. Manager basics. This is a cool 72. Uh huh.

So we have DX over. So integral FDX over three minus five x to the power off four. I went looking here. I would think of doing substitution. So you is three minus five x. So do you. Over. DX is minus five. So d x is do you over Negative five. Now, remember, this can also be read as integral off three minus five X to the minus four DX. So now let's move on from there. Let's substitute. So that's integral. A few to the negative four, do you? Over. Negative five. Those This becomes minus 1/5. Just factor 1/5 out into grow. A few to the minus four. Okay, Now, uh, let's add one to the power. So integrating that'll be minus one of five times you to the minus three over minus three. So that's Ah minus you to the negative three. Over. Minus 15. Now we're not done yet because you is three minus five x. So let's put that in here. So three minus five x. So my to the minus three over negative 15 which is also three minus five x to the minus three over 15 plus c. So this is your final answer here

7.1 dot seven. So we're asked to perform the integration. Um, won over three monies. Five x rays to the fourth power said the key years. My substitution. I'm gonna let you equal three minus five x. That means that do you is equal to minus five. The X So what I want to see in this integral I want to see you and do you so I can make substitution. Well, in order to make this substitution if I write minus five d x over three minus five x to the fourth DX. If I multiply that by minus five, I also have to divide by minus fire. So this is an equivalent integral. But what you see here is that I'm sorry about this. I didn't need to write DX twice, minus five D X. You see that is, do you? And then what you see here? This is, um, in the bottom. That is you to the fourth power. So this transforms to minus one fifth, and then you see the Negro of, um, one over. And this is you to the fourth, do you? So this is minus 1/5 in a row. A lot of times. It's just easier to write this, um, without fractions. So you to the minus four. How do you integrate this? So this is minus 1/5 to integrate you to the minus fourth. You increment the exponents at positive direction by one. So that's going to be you to the minus third power. And then you divide by that exponents of minus 1/3. And so this just becomes 1/15 you to the minus three, plus a constant of integration. So that's my final answer after the integration. But in terms of the variable you I needed to be in terms of the variable of x. So x, remember you was three minus five x. So this final answer becomes one over 15 three minus five x cubed, plus constant of integration.


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