Question

help with integrals!

Answer 1

\[\int\limits_{3x}^{x^4}t^2dt\] then f'(x)=?

Answer 2

\[f(x)=\int\limits_{a(x)}^{b(x)} g(t) dt=G(t)|_{a(x)}^{b(x)}=G(b(x))-G(a(x)) \\ \text{ where } G'=g \\ \text{ differentiating } f(x) \\ \text{ we get ... } \\ f'(x)=b'(x) \cdot G'(b(x))-a'(x) \cdot G'(a(x)) \text{ by chain rule } \\ f'(x)=b'(x)g(b(x))-a'(x)g(a(x)) \text{ since } G'=g\]

Answer 3

thanks, I forgot about the chain rule

Answer 4

np