Learn how to solve problems step by step online. Integrate the function y^2(2b-y)^(1/2) from 2b to b. We can solve the integral \int_{2b}^{b} y^2\sqrt{2b-y}dy by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 2b-y it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dy in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by finding the derivative of the equation above. Isolate dy in the previous equation. Rewriting y in terms of u.

Integrate the function y^2(2b-y)^(1/2) from 2b to b