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(25 pts:) Solve the integral equationy(t) = 8 _ 15 K sin(Su)y(t u) du. Justify your answer...

Question

(25 pts:) Solve the integral equationy(t) = 8 _ 15 K sin(Su)y(t u) du. Justify your answer

(25 pts:) Solve the integral equation y(t) = 8 _ 15 K sin(Su)y(t u) du. Justify your answer



Answers

Solve for $K,$ given that \int_{1}^{2}\left[\left(3 x^{2}+5 x\right)-(3 x+K)\right] d x=6

In discussion with the corner you have integral off the small F x and X. Supposed this one equal to the capital FX. And this equivalent this equation equivalent to the I have a prime of X here must go to the small FX. It is question were given the integral on the seven. Our eight minus X our far the X on were given this unequal to the gay off eight minus X power three plus a constancy we can think of this will be in the small FX. On the haunting him will be the capital FX. So this equation you will be equivalent to the gay over eight, minus X power three plus c the river to hear must equal to the 7/8 months X power far. Now let's try to do this derivative. Okay, we stay the same. This one we can turn into the okay. Eight minus three. Okay, eight minutes. Expo minus three. A blind. The power rule. We can 80 minutes X minus minus three minutes on B minus far by the general. We need to attempt the derivative on the inside here, which is equal to minus one that the roof. The on the city. Could you zero. Then we get equal to the 708. Minus next. How far we can rewrite this now into the minus one. Over minus K over eight. Minus X power Far. It must equal to the 7/8 minus X. Our power Far from here. We see that doesn't symbolized. The minus game is equal to the seven. Ah, the game was equal to minus seven.

In this question would record abound Anti derivative of any constant? I would call it I said I d X and then we can get equal to the A X plus a constancy in this question were given the integral on the case square the X And we're telling that the K here will be the constants. So it means that they can hear case quite exactly with in this formula they're found by the formula 100 k square X plus a constancy.

In this question. Were you calling about anti derivative of the the Okay, X, the X I get nickel to one of a k each of the K X plus a constancy in discussion, given the integral five each of the Manus to de de de here we can. First of all, I will bring the five outside the integral to kind of five in the ground that even I managed to the the day. And then here we can identify the minus two will be the guy in the formula. Therefore again go to the five times one over minus two aged minus toothy plus the constancy and we signify got the minus five out of two age the Manus toothy plus c. And now, by question, once you make this one ICO to you that guy, each of the manage to the policy, so it will compare them. We see that the guy here must equal to this number here. So it means that they must be equal to minus five out of two

In discussion here will record that you have the integral off the function f x t x equal to the capital. F X doesn't it will equivalent to the F X capital of Prime. It will go to this month. FX, in this question, were given the integral off the three X plus Jew by for the X and it got to the gay temps three x plus two about five plus c. If we can identify, this, one will be the small f x. The haunting here will be the capital F X Yeah, this equation will be equivalent to the gay three x plus two about five plus c Everything here the Riverdale it must equal to the three express to oh fall and let's try to do the degree with you. Now we will have the case stays the same by the power will have the five three X plus two five minutes When you go too far and by the general, we need two times the derivative on the three X plus two, which is three now. The river, the undersea equal to zero equal to the tree express to about far It would be right this. Then we get equal to the gay 53 So equal to the 15 gay times three X plus two four equal to the tree. Expressed you well, far from here we see we can identify this one equal to no one in front here. So it means that 15 games equal to one Our game is equal to one hour 15.


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