Which of the following definite integrals vanish?

MATHEMATICS · Multi correct · CBSE · Mathematics · Integrals · Integrals

Problem

Which of the following definite integrals vanish? (1)

\int_{0}^{\pi/2}\ln(\cot x)\,dx

(2)

\int_{0}^{2\pi}\sin^3x\,dx

(3)

\int_{1/e}^{e}\frac{dx}{x(\ln x)^{1/3}}

(4)

\int_{0}^{\pi}\sqrt{\frac{1+\cos 2x}{2}}\,dx