1
IIT-JEE 1985
Subjective
+5
-0
Sketch the region bounded by the curves $$y = \sqrt {5 - {x^2}}$$ and $$y = \left| {x - 1} \right|$$ and find its area.
2
IIT-JEE 1984
Subjective
+2
-0
Evaluate the following $$\int\limits_0^{{1 \over 2}} {{{x{{\sin }^{ - 1}}x} \over {\sqrt {1 - {x^2}} }}dx}$$
3
IIT-JEE 1984
Subjective
+4
-0
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.
4
IIT-JEE 1984
Subjective
+4
-0
Find the area of the region bounded by the $$x$$-axis and the curves defined by $$y = \tan x, - {\pi \over 3} \le x \le {\pi \over 3};\,\,y = \cot x,{\pi \over 6} \le x \le {{3\pi } \over 2}$$\$
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