## ns36 3 years ago What's the integral of (2-x)^(1/2)?

use substitution, i.e.:$u=2-x\tag{a}$therefore:$du=-dx$therefore:$\int (2-x)^{\frac{1}{2}}dx=-\int u^{\frac{1}{2}}du=-\frac{2u^{\frac{3}{2}}}{3}+constant$then substitute back using equation (a) to get:$\int (2-x)^{\frac{1}{2}}dx=-\frac{2(2-x)^{\frac{3}{2}}}{3}+constant$