COMPASSLearning

Talk to us Register Login

CBSE Class 12 · 2011 · Definite IntegralsLong Answer

Evaluate:

\int_{π /6}^{π /3} \frac{d x}{1 + t a n x}

Answer: $\frac{π}{12}$

Solution

Let

I = \int_{π /6}^{π /3} \frac{d x}{1 + tan x}

. The limits satisfy

a + b = \frac{π}{2}

, so apply

f (x) \to f (a + b - x)

with

tan (\frac{π}{2} - x) = cot x

:

I = \int_{π /6}^{π /3} \frac{tan x}{1 + tan x} d x

Adding:

2 I = \int_{π /6}^{π /3} d x = \frac{π}{3} - \frac{π}{6} = \frac{π}{6}

, so

I = \frac{π}{12}

.

CBSE Class 12 Board · 2011 · Subjective

Practise more: all CBSE board PYQs on Definite Integrals →

More board questions on Definite Integrals

The value of $\int_{π /4}^{π /2} cot θ cosec^{2} θ d θ$ is
CBSE 2024View solution →
Evaluate: $\int_{0}^{π} \frac{e ^{c o s x}}{e ^{c o s x} + e ^{- c o s x}} d x$
CBSE 2024View solution →
Evaluate $\int_{l o g 2}^{l o g 3} \frac{1}{( e ^{x} + e ^{- x} ) ( e ^{x} - e ^{- x} )} d x$
CBSE 2023View solution →
Evaluate $\int_{- 1}^{1} x^{4} - x d x$
CBSE 2023View solution →
Evaluate $\int_{0}^{π /2} \frac{1}{1 + ( t a n x ) ^{2/3}} d x$
CBSE 2022View solution →
$\int_{- \frac{π}{4}}^{\frac{π}{4}} sec^{2} x d x$ :
CBSE 2020View solution →