Question

What is `int_(0)^(1) e^(5x)dx`?

Answer 1

`1/5(e^5-1)`

Explanation:

Using the substitution technique :

Let `u=5x`. Then `du = 5dx =>1/5du=dx`

Limits : `x=0=>u=0 and x=1=>u=5`

Therefore the original integral becomes

`1/5int_0^5e^udu=1/5[e^u]_0^5=1/5(e^5-1)`