Question

Need help with this problem

Answer 1

I got the answer (2x^7)(7x^6)-(2x^5)(5x^4) but it is not correct..

Answer 2

@dan815

Answer 3

evaluate the definite integral with those bounds , then take the derivative of the polynomial

Answer 4

distribute the ( ) out then integrate

Answer 5

\[F(x)=\int\limits_{a(x)}^{b(x)}g(t)dt=G(t)|_{a(x)}^{b(x)} \\ F(x)=G(b(x))-G(a(x)) \\ \text{ differentiate both sides } \\ F'(x)=b'(x)G'(b(x))-a'(x)G'(a(x)) \text{ recall } G'=g \\ F'(x)=b'(x)g(b(x))-a'(x)g(a(x))\]
you will notice I used chain rule to differentiate

Answer 6

the integral evaluates to

2x^28 -4x^21 -2x^20 +4x^15 + 3x^14 -3x^10 - x^7 + x^5

differentiate that

Answer 7

just integrate and sub in bounds then derive