a-x-x-t-5-y-t-dt-4x-6-y-x-

Question Number 26584 by gunawan last updated on 27/Dec/17

\int_{a}^{x} {(x - t)}^{5} y (t) d t = 4 x^{6}

y (x) = \dots

Commented by prakash jain last updated on 27/Dec/17

\frac{d}{d x} \int_{a (x)}^{b (x)} f (x, t) d t

= f (x, b (x)) \frac{d}{d x} b (x) - f (x, a (x)) \frac{d}{d x} a (x) +

\int_{a (x)}^{b (x)} \frac{\partial}{\partial x} f (x, t) d t

\frac{d}{d x} a (x) = 0

f (x, x) = 0

4 \cdot 6 \cdot x^{5} = \int_{a}^{x} 5 {(x - t)}^{4} y (t) d t

4 \cdot 6 \cdot 5 \cdot x^{4} = \int_{a}^{x} 5 \cdot 4 {(x - t)}^{3} y (t) d t

c o n t i n u e t o g e t

24 x = \int_{a}^{x} y (t) d t

Commented by prakash jain last updated on 27/Dec/17

Do you have the final answer ?

i am not able to get to a final answer .

Commented by prakash jain last updated on 27/Dec/17

F (x) = \int_{a}^{x} {(x - t)}^{5} y (t) d t = 4 x^{6}

F (a) = \int_{a}^{a} {(a - t)}^{5} y (t) d t = 0

\Rightarrow 4 a^{6} = 0 \Rightarrow a = 0

c a n y o u p l e a s e c h e c k q u e s t i o n

i f a = 0, y = 24

Commented by prakash jain last updated on 28/Dec/17

Integrate after puttimg y = 24 .

Also value of a can only be 0 . Since

F (a) = 0 .