# Integral Evaluation

1. Jul 31, 2007

### ehrenfest

1. The problem statement, all variables and given/known data
How would you evaluate

$$\frac{d}{dx} \int _{x}^{tanx}exp(-t^2)dt$$ ?

2. Relevant equations

3. The attempt at a solution

So I think you want to substitute variables int order to get the lower limit a constant and the upper limit a variable with constant derivative. Then we just take out the derivative operator and the integral sign. I just cannot think of the right substitution...

Last edited: Jul 31, 2007
2. Jul 31, 2007

### bel

let $$\int exp(-t^2)dt = F(t)$$,

then, $$\int _{x}^{tanx}exp(-t^2)dt = F(tanx)-F(x)$$

then use the chain rule to differentiate, since you already know the derivative of $$F(x)$$.

3. Jul 31, 2007

### ehrenfest

That works. Thanks.