1
IIT-JEE 1989
Subjective
+5
-0
Find all maxima and minima of the function $$$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$
Also determine the area bounded by the curve $$y = x{\left( {x - 1} \right)^2}$$,
the $$y$$-axis and the line $$y-2$$.
2
IIT-JEE 1989
Subjective
+3
-0
Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$
3
IIT-JEE 1989
Fill in the Blanks
+2
-0
The value of $$\int\limits_{ - 2}^2 {\left| {1 - {x^2}} \right|dx} $$ is ...............
4
IIT-JEE 1989
Subjective
+4
-0
If $$f$$ and $$g$$ are continuous function on $$\left[ {0,a} \right]$$ satisfying
$$f\left( x \right) = f\left( {a - x} \right)$$ and $$g\left( x \right) + g\left( {a - x} \right) = 2,$$
then show that $$\int\limits_0^a {f\left( x \right)g\left( x \right)dx = \int\limits_0^a {f\left( x \right)dx} } $$
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