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
2
IIT-JEE 1984
Subjective
Given a function $$f(x)$$ such that
(i) it is integrable over every interval on the real line and
(ii) $$f(t+x)=f(x),$$ for every $$x$$ and a real $$t$$, then show that
the integral $$\int\limits_a^{a + 1} {f\,\,\left( x \right)} \,dx$$ is independent of a.
Answer
Solve it.
3
IIT-JEE 1984
Subjective
Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx} $$
Answer
$${{6 - \pi \sqrt 3 } \over {12}}$$
4
IIT-JEE 1983
Subjective
Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and
the ordinates at $$x=2$$ and $$x=4$$. If the ordinate at $$x=a$$ divides the area into two equal parts, find $$a$$.
Answer
$$a = 2\sqrt 2 $$
Questions Asked from Definite Integrals and Applications of Integrals
On those following papers in Subjective
Number in Brackets after Paper Indicates No. of Questions