Calc.2 Evaluating the indef. integral...

Evaluate the indefinite integral

Evaluate the indefinite integral

Integral of x^2dx/sqrt 64-x^2

∫x²/√(64 - x²) dx

Make a trig sub and substitute x = 8*sin(t). Integral becomes:

∫(64*sin²(t)*8*cos(t))/(8*cos(t)) dt

∫64*sin²(t) dt

32*∫(1 - cos(2t)) dt

32t - 16*sin(2t) + C

32t - 32*sin(t)*cos(t) + C

32*arcsin(x/8) - 32(x/8)(√(64 - x²)/8) + C

32*arcsin(x/8) - x√(64 - x²)/2 + C