# Integration of many variables

## Homework Statement

Let
F(x) = integral from x to 1 ( $$3t^3 - x^2 t ) dt$$

1. Calculate F'(x)

## The Attempt at a Solution

I know the answer is

x^3 + x.

However, I am not sure how it is obtained.

I know about implicit differentian, but I have never done implicit integration.

How can you solve the problem?

## Answers and Replies

CompuChip
Homework Helper
In this case, you can simply work out the integral.
Do the t-integration, it will give you
$$\frac34 t^4 - \frac12 x^2 t^2$$
evaluated between the boundaries t = x and t = 1.
Then differentiate.

In this case, you can simply work out the integral.
Do the t-integration, it will give you
$$\frac34 t^4 - \frac12 x^2 t^2$$
evaluated between the boundaries t = x and t = 1.
Then differentiate.