evaluate the definite integral

Question

Evaluate the definite integral

 

 a

∫−2x√(x^2+a^2) dx

-a

Answer 1

I agree with Kenneth S. that since the integrand is an odd function of x, and the integral, call it I, is between symmetrically placed limits, -a and a, the result should be, even without any detailed calculations, I = 0.