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1

IIT-JEE 1988

Subjective
Evaluate $$\int\limits_0^1 {\log \left[ {\sqrt {1 - x} + \sqrt {1 + x} } \right]dx} $$

Answer

$${1 \over 2}\left[ {\log 2 + {\pi \over 2} - 1} \right]$$
2

IIT-JEE 1988

Subjective
Find the area of the region bounded by the curve $$C:y=$$
$$\tan x,$$ tangent drawn to $$C$$ at $$x = {\pi \over 4}$$ and the $$x$$-axis.

Answer

$${1 \over 2}\left[ {\log 2 - {1 \over 2}} \right]$$ sq. units
3

IIT-JEE 1987

Subjective
Find the area bounded by the curves, $${x^2} + {y^2} = 25,\,4y = \left| {4 - {x^2}} \right|$$ and $$x=0$$ above the $$x$$-axis.

Answer

$$4 + 25{\sin ^{ - 1}}{4 \over 5}$$
4

IIT-JEE 1986

Subjective
Evaluate : $$\int\limits_0^\pi {{{x\,dx} \over {1 + \cos \,\alpha \,\sin x}},0 < \alpha < \pi } $$

Answer

$${{\pi \alpha } \over {\sin x}}$$

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Class 12