Evaluate the definite integral x times the √x -1 from 0 to 4

Question

Definite Integrals

Answer 1

∫_{(0 to 4)} [x(√x - 1)]dx = ∫_{(0 to 4)} [x^3/2 - x^1/2]dx = [(2/5)x^5/2 - (2/3)x^3/2]_{(0 to 4)}

= [(2/5)(4)^5/2 - (2/3)(4)^3/2 ] - 0 = 64/5 - 16/3 = 112/15