JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

Let

f:R \to R

be a differentiable function such that

f\left( {\frac{\pi }{4}} \right) = \sqrt 2 ,\,\,f\left( {\frac{\pi }{2}} \right) = 0

and

f'\left( {\frac{\pi }{2}} \right) = 1

and let

g\left( x \right) = \int_x^{\frac{\pi }{4}} {\left( {f'\left( t \right)\sec t + \tan t\sec t\left( t \right)} \right)} dt

for

x \in \left[ {\frac{\pi }{4},\frac{\pi }{2}} \right).

Then

\lim\limits_{x \to {{\left( {\frac{\pi }{2}} \right)}^ - }} g\left( x \right)

is equal to

View answer and explanation

Correct option: B

Option B (3) is correct because the limit of

g(x)

x

approaches

\frac{\pi}{2}

from the left is found by substituting

x = \frac{\pi}{2} - h

and applying L'Hôpital's rule, resulting in 3.

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