Answer to Question #162016 in Calculus for Phyroe

Question

Evaluate the ∫y(y²-2)²dy

Answer 1

Solution

∫y(y²-2)²dy = (1/2) ∫(y²-2)²dy²

Substitution x = y² => ∫y(y²-2)²dy = (1/2) ∫(x-2)²dx = (1/2) ∫(x-2)² d(x-2) = (x-2)³ /6 + C =   (y²-2)³ /6 + C

Answer

∫y(y²-2)²dy = (y²-2)³ /6 + C