Question

h(x)=∫sqrt(1+t^4) on the interval [x^2, 2], find h'(1)
a. -2sqrt(2)
b. sqrt(2)
c. -sqrt(2)
d. 2(sqrt2)
e. 4sqrt(2)

Answer 1

so \[h(x)=\int\limits\limits_{x^2}^{2} \sqrt{1+t^4} \] = \[F(2)-F(x^2)\] ?

Answer 2

Or should i use the second fundamental theorem?

Answer 3

\[\Large\bf\sf h'(x)\quad=\quad \frac{d}{dx}\left[F(2)-F(x^2)\right]\]No it looks like you've got the right idea so far! :)

Answer 4

First Fundamental Theorem.

Answer 5

Take your derivative, applying the chain rule,\[\Large\bf\sf h'(x)\quad=\quad 0-f(x^2)\cdot 2x\]

Where \(\Large\bf\sf \quad f(x)\quad=\quad \sqrt{1+t^4}\)