GATE 2023 ES – Question 33
Evaluate $(4/\pi)\int_0^{\pi/2}\sin^2x\,dx$,to two decimals.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 1.00 to 1.00
Explanation
Use $\sin^2x=(1-\cos2x)/2$. The integral is $[x/2-\sin2x/4]_0^{\pi/2}=\pi/4$. Multiplying by 4/π gives exactly **1.00**. The prefactor belongs outside the integral and cancels its π dependence.