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CBSE Class 12 · 2024 · Definite IntegralsMultiple Choice

The value of

\int_{π /4}^{π /2} cot θ cosec^{2} θ d θ

is

(A) $\frac{1}{2}$ ✓ Correct
(B) $- \frac{1}{2}$
(C) $0$
(D) $- \frac{π}{8}$

Answer: (A)

Solution

Put

t = cot θ \Rightarrow d t = - cosec^{2} θ d θ

. When

θ = \frac{π}{4}, t = 1

; when

θ = \frac{π}{2}, t = 0

.

\int_{π /4}^{π /2} cot θ cosec^{2} θ d θ = \int_{1}^{0} t (- d t) = \int_{0}^{1} t d t = [\frac{t ^{2}}{2}]_{0}^{1} = \frac{1}{2}

Correct option: (A)

\frac{1}{2}

.

CBSE Class 12 Board · 2024 · Single correct option

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