Find the derivative of the function

integral from 4x to 7x of (u^2-1)/(u^2+1)

Question

Find the derivative of the function

integral from 4x to 7x of (u^2-1)/(u^2+1)

anonymous · Answer

$$\int\limits_{4x}^{7x} \frac{ u^2-1 }{ u^2 + 1 }$$

anonymous · Answer

are u sure the problem like that ??

anonymous · Answer

I'm suppose to find the derivative of that integral

anonymous · Answer

yea i see.. but actually if using  u's variables, so we use sign du.. but there i cant see du or dx ?

anonymous · Answer

Yeah I have no idea how to approach this problem because u-substitution wouldn't apply

anonymous · Answer

summon or tag @Hero , @hartnn ....

hero · Answer

Is it du or dx?

anonymous · Answer

du

hero · Answer

Okay

hero · Answer

Integral and Derivative are inverses of each other, so you end up with the the original function you came up with including the limits of integration:

$$\left[ \frac{u^2-1}{u^2+1} \right]^{7x}_{4x}$$

hero · Answer

Then continue evaluating:
$$\left[ \frac{u^2-1}{u^2+1} \right]^{7x} - \left[ \frac{u^2-1}{u^2+1} \right]_{4x}$$

hero · Answer

$$\left[ \frac{(7x)^2+1}{(7x)^2-1} \right] - \left[ \frac{(4x)^2+1}{(4x)^2-1} \right]$$

hero · Answer

I'm pretty sure you can finish that on your own.

anonymous · Answer

thank you

hero · Answer

yw