Question

If $I_{1} = \int\limits^{3\pi}_{0}f\left(\cos^{2}\,x\right)dx$ and $I_{2} = \int\limits^{\pi}_{0} f\left(\cos^{2}\,x\right)dx$, then

• A. $I_1 = I_2$
• B. $3I_1 = I_2$
• C. $I_1 = 3I_2$
• D. $I_1 = 5I_2$

Answer 1

Answer: (C)

$I_1 = 3I_2$

Answer 2

$I_{1}=3 \int\limits_{0}^{\pi} f\left(\cos ^{2} x\right) d x=3 I_{2}$
$[\because$ period is $\pi]$