- #1

LilTaru

- 81

- 0

## Homework Statement

Differentiate the following functions with respect to x.

a) [tex]\int[/tex] (t

^{2}+ cos(t

^{7}))/(1 + t

^{4}) dt [0, x]

b) [tex]\int[/tex] (t

^{2}+ cos(t

^{7}))/(1 + t

^{4}) dt [2, x]

c) [tex]\int[/tex] (t

^{2}+ cos(t

^{7}))/(1 + t

^{4}) dt [0, sin x]

d) [tex]\int[/tex] (t

^{2}+ cos(t

^{7}))/(1 + t

^{4}) dt [x, sin x]

e) [tex]\int[/tex] (x

^{2}+ cos(t

^{7}))/(1 + x

^{4}) dt [2, sin x]

Note: [a, b] means a is the lower limit of the integral and b is the upper limit of the integral.

## Homework Equations

I know that the derivative of an indefinite integral is the function itself and that with definite integrals you need to find an antiderivative G(x) and the derivative equals G(upper limit) - G(lower limit).

## The Attempt at a Solution

I have no idea how to find an antiderivative for this function. Nor do I know how to use sin(x) as an upper limit. Nor do I know how to do (e) with x replacing some of the t's. Will x be considered a constant then, since we are differentiating in respect to t? I don't want the answers to all of them... I prefer to do the work on my own... That's how I actually learn, but if someone can give me a hint on how to start each one? I would be greatly appreciative!