Question

What's the integral of (2-x)^(1/2)?

Answer 1

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:\[\int (2-x)^{\frac{1}{2}}dx=-\frac{2(2-x)^{\frac{3}{2}}}{3}+constant\]