JEE Main 2022 · 28 Jul · Shift 2 · Mathematics Q90

MathematicsInteger+4 / -1Question 90 of 90

The value of the integral $\displaystyle\int_0^{\pi/2}60\frac{\sin(6x)}{\sin x}dx$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 104

Identity. $\frac{\sin6x}{\sin x}=2(\cos5x+\cos3x+\cos x)$ .

Integrate on $[0,\frac\pi2]$ : $2\left(\frac15-\frac13+1\right)=\frac{26}{15}$ ; times 60 is 104.

Answer: 104

JEE Main 2022 · 28 Jul · Shift 2, Mathematics question 90