Question

Integrate sqrt(1 - x) dx from 0 to 1

Answer 1

Hi,

`(2)/(3)`

Explanation:

Let's assume

`t^2=1-x\\2t\ dt=-1*dx\\\int\limits^1_0 {√(1-x)\ \, dx =\int\limits^0_(-1) {t*(-2t)} \, dt =-2[(t^3)/(3) ]_(-1)^(\ 0)=(2)/(3)`