Evaluate the following improper integral

Question

∫(1-2x) ⁄√(x-x²)dx

with upper limit as 1, and lower limit as 0

Any assistance would be appreciated. Thank you !

Answer 1

∫₀¹(1-2x) ⁄√(x-x²)dx = 2√x-x²₀¹ = 0 - 0 = 0

Integral we evaluate using substitution u = x - x²