5

Find thelfollowing integralsy @a) f (3xm+ 5x2htl 2)dxh)f (3x2 + 5Vx)dx1) J (t3k2t] 3)dt0 ( (2e* + 5 + In2)c) f (emzx)dx1 [(2x + Sdxd) [ ( #8emx)dxk)J? (2x +x?)axe) ...

Question

Find thelfollowing integralsy @a) f (3xm+ 5x2htl 2)dxh)f (3x2 + 5Vx)dx1) J (t3k2t] 3)dt0 ( (2e* + 5 + In2)c) f (emzx)dx1 [(2x + Sdxd) [ ( #8emx)dxk)J? (2x +x?)axe) [ (7e-*1 H) axD 8c t')dt0 [ (2x? + 3x - 5 +1 #)dx g)f( # 4 dxm) [2 (2e5 #)at

Find thelfollowing integralsy @a) f (3xm+ 5x2htl 2)dx h)f (3x2 + 5Vx)dx 1) J (t3k2t] 3)dt 0 ( (2e* + 5 + In2) c) f (emzx)dx 1 [(2x + Sdx d) [ ( #8emx)dx k)J? (2x +x?)ax e) [ (7e-*1 H) ax D 8c t')dt 0 [ (2x? + 3x - 5 +1 #)dx g)f( # 4 dx m) [2 (2e5 #)at



Answers

Let $F(x)=\int_{0}^{x} p(t) d t$ and $G(x)=\int_{3}^{x} p(t) d t,$ where $F(3)=5$ and $G(5)=7 .$ Find each of the following. (a) $\quad G(0)$ (b) $\quad F(0)$ (c) $\quad F(5)$ (d) $k$ where $G(x)=F(x)+k$

In the institution we have given the value that it affects is equals two. Integration of three actually square minus X plus seven upon X -1 to the Power seven. And it is told that or into F of zero plus five is equal to zero. And we have to find the coefficient of x square in four x -1 to the Politics FX. So first of all, I I am going to solve This portion. So here I am assuming that Y is equal to X -1. So we can say that X can be written as Y plus one or dx will because to day Y supporting the avoid function. So the effects will be returned as this is integration three and two Y plus one. Holy square minus Y plus one last seven upon this is why do the Power seven into Dy now I'm going to simplify the situation so this will comes out to be three y squared plus five five. Last nine. Upon why do the power seven B. Y. Now I'm going to separate this portion so this can be written as three white to depart -5 plus five. Into right to the par minus six plus nine into right to the par minus seven. Do I? Now I'm going to integrate this and I will get this is minus three Y squared because four y plus six upon four. Right to the power six plus constant. Now we can now I'm again putting the value of Y. Your support. Why is he close to X minus one. So this will finally Convert into effective equals two minus of three X squared minus two X plus five Upon this is X -1 to the power 16-4 plus constant. C. So this is the value of FX. We have given that at F zero The venue is -5 x four plus, this is constancy. And we have given that four, Plus five is equal to zero. So now put the value of F0 here so we get she is equal to zero. This is the value of C. So finally our function effects will be we've done this Renect is equals two two x minus three X squared minus five. Upon four X -1 to the Power six. No, I can write it as four X -1. to the politics into FX is he goes to disease works minus three X squared -5. We have to find the coefficient of Axis Square. So coefficient of access where we can clearly see that is -3 -3 is the answer of our given to shin and it is given an option b. So this is the answer for this. Given to shin. Thank you.

In the given question there is the integration. The Interior Decoration start of -2 25 And it is if access were ex idiots we have to represent it in the former. They're too big. Okay. Yes we need to look. Okay. And we want to find the substitution W. A. B. And cared. So you can look here. Clearly let I assume that this integration is I. And I substitute here 30 place of access square W. So that I could get F. W. It's the relative provides a way to work for the accepting studio develop. This shows that actually exceeded replaced by idea of the way to. Okay now I have to think for limits. Also because the all the limited stands for X. And we have to find for W. So when X is -2 or when exceeds five then what is the value of When you put here -2 you get square of -2 that is four. And if you put a refined then you get five square 13 25. Okay. No way put all these substitutions in the integration then I get the integration 4- 25. And any place of access where w so the blue narrative place of X. Dx did a blue belt. Now again this can with his bitterness 4-25 one bite after we loaded. Now you compare it with our given integration. It is they're to be K F W DW by comparison. You can see that there is for base 25 K's. One by two. And We had a wild case here. one x 2. Okay Case one Vital and W We had taken He's equals two. It's just what? So these are all the we lose here. Okay thanks.

However, the work here the function that Facebook you invite. Okay. Middle while do a square like you handle saying off they killed d d. We need to find function with respect to X hang with respect away So first you need to find with Rose Perfect. Is there a bigger thing? It best No thanks. Easy political Be by the ex self back to square like you into So I enough exist Square like killed the whole cube Light up debate be excel Bargaining do side enough Martin. Thank you. What is it caused to Cool X like you say enough excess to think Where is too light credit to find if What for f late it was B But be well Pick the square like you in Do say you know it's a square. I killed the whole cube. Why does day But the way off Why I didn't go So you know we learn killed. So with your bigger thing it best Do you pick the square life? Where saying off excess to think India players to land

In the given question and there is the integration within the limits of 2-5 and the integration is half of Ireland Access square this one okay in blue exactly where to buy access where that's where index we are to represent this in the form of here to be K F W. Data to do that. Let this integration is equal to weigh. I substitute here I learned off axis where plus when it was to w if the relatives should be When a bone access for plus one into two accents the X equals two. Data shows me that X divided by access we're blessed be X can be replaced by two. W wait. Oh okay no vehicle think about the new limits also because the old one stands for ex the gold star for X. So when access took or when X is five and then you were to find W. Year. But on this situation I can say that the new year should be Flow of those witness one it was to global fight and he has global five squared minus one. That is not all of 26. Okay. No we make all these substitutions in the integration than our integration Should have. New limits low 5 to glock 26. Or it can also be written us a letter. Sorry? Yes. Helena five To Hell Enough 26. And at the place of dysfunction here to put the blue in the loop and that the place of you're exit divided by Access. We're blessed one and DX you have to put it on the word. Oh no we compare it with the given integration. That is to be okay. W w we're comparing both the sides. We conclude that first of all for the limits A. And B. Here. Elena five And a line of 26 and K. Constant here is one way to and the blue function. He were already taken to solve ways. I can say that two days Learner Access where last one okay. They know on the answers here, I think.


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