Question

What is the antiderivative of `y=sqrt(x)` from 0 to 5?

Answer 1

`(2sqrt(125))/3`

Explanation:

`int_0^5sqrtxdx=int_0^5(x)^(1/2)dx->`We want to convert the function into index form so that we can apply simple power rules.

`int_0^5(x)^(1/2)dx=[(2x^(3/2))/3]_0^5`

`=[(2(5)^(3/2))/3]-[0]`

`=(2(5)^(3/2))/3=(2sqrt(125))/3`