The value of $\mathop \smallint \limits_0^{\pi /2} \,\,\frac{{{{\sin }^3}\,\,x\,\,\cos \,\,x}}{{{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x}}\,\,dx$, is

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

1 of 1

Application +4 | -1

The value of

\int \limits_0^{\pi /2} \,\,\frac{{{{\sin }^3}\,\,x\,\,\cos \,\,x}}{{{{\sin }^4}\,\,x\,\, + \,\,{{\cos }^4}\,\,x}}\,\,dx

, is

View answer and explanation

Correct option: A

\pi /8

Option A (π/8) is correct because by using the property of definite integrals and trigonometric identities, the integral simplifies to π/8.