Calculus Question

Question

Explain in detail why the integral, ∫¹₀ (-2x/1-x²)dx, cannot be evaluated.

Answer 1

The antiderivative of the integrand is the logarithm function ln|1-x^2|.

By the definition of the improper integral we have that your integral equals to the limit of (integral from 0 to b) (-2x/(1-x^2)) dx as b goes to 1. But this equals ln|1-b| which goes to -\infty as b goes to 1 since the logarithmic function is not defined at the value 0.