Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}} $$ and $$y = \left| {x - 1} \right|$$ and find its area.
Answer
$${{5\pi - 2} \over 4}$$ sq. units
3
IIT-JEE 1985
Subjective
Evaluate the following : $$\,\,\int\limits_0^{\pi /2} {{{x\sin x\cos x} \over {{{\cos }^4}x + {{\sin }^4}x}}} dx$$
Answer
$${{{\pi ^2}} \over {16}}$$
4
IIT-JEE 1984
Subjective
Find the area of the region bounded by the $$x$$-axis and the curves defined by
$$$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$$
Answer
$$\log {3 \over 2}$$ sq. units
Questions Asked from Definite Integrals and Applications of Integrals
On those following papers in Subjective
Number in Brackets after Paper Indicates No. of Questions