If 𝑓 is continuous and (1,8)∫𝑓(𝑡)𝑑𝑡=16, find the integral (1,2)∫𝑡^2𝑓(𝑡^3)𝑑𝑡

Answer 1

∫₁²t²f(t³)dt = 1/3∫₁⁸f(z)dz = 1/3·16 = 16/3 substitution: t³ = z; dt = dz(3t²)

t = 1, z = 1; t = 2 z = 8