First slide

Evaluation of definite integrals

Question

If $P = \int_{0}^{3 π} f (\cos^{2} x) dx and Q = \int_{0}^{π} f (\cos^{2} x) dx$ then

Moderate

A

$P - Q = 0$
B

$P - 2 Q = 0$
C

$P - 3 Q = 0$
D

$P - 5 Q = 0$

Solution

Given, $P = \int_{0}^{3 π} f (\cos^{2} x) dx$ …..(i)
and $Q = \int_{0}^{π} f (\cos^{2} x) dx$ …….(ii)
From Eq.(i),
$\begin{aligned} P = 3 \int_{0}^{π} f (\cos^{2} x) dx \\ \Rightarrow P = 3 Q \Rightarrow P - 3 Q = 0 \end{aligned}$

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