1

IIT-JEE 1999

Subjective

+10

-0

Let $$f(x)$$ be a continuous function given by
$$$f\left( x \right) = \left\{ {\matrix{
{2x,} & {\left| x \right| \le 1} \cr
{{x^2} + ax + b,} & {\left| x \right| > 1} \cr
} } \right\}$$$

Find the area of the region in the third quadrant bounded by the curves $$x = - 2{y^2}$$ and $$y=f(x)$$ lying on the left of the line $$8x+1=0.$$

2

IIT-JEE 1997

Subjective

+5

-0

Let $$f(x)= Maximum $$ $$\,\left\{ {{x^2},{{\left( {1 - x} \right)}^2},2x\left( {1 - x} \right)} \right\},$$ where $$0 \le x \le 1.$$

Determine the area of the region bounded by the curves

$$y = f\left( x \right),$$ $$x$$-axes, $$x=0$$ and $$x=1.$$

Determine the area of the region bounded by the curves

$$y = f\left( x \right),$$ $$x$$-axes, $$x=0$$ and $$x=1.$$

3

IIT-JEE 1996

Subjective

+3

-0

Let $${A_n}$$ be the area bounded by the curve $$y = {\left( {\tan x} \right)^n}$$ and the

lines $$x=0,$$ $$y=0,$$ and $$x = {\pi \over 4}.$$ Prove that for $$n > 2,$$

$${A_n} + {A_{n - 2}} = {1 \over {n - 1}}$$ and deduce $${1 \over {2n + 2}} < {A_n} < {1 \over {2n - 2}}.$$

lines $$x=0,$$ $$y=0,$$ and $$x = {\pi \over 4}.$$ Prove that for $$n > 2,$$

$${A_n} + {A_{n - 2}} = {1 \over {n - 1}}$$ and deduce $${1 \over {2n + 2}} < {A_n} < {1 \over {2n - 2}}.$$

4

IIT-JEE 1995

Subjective

+5

-0

Consider a square with vertices at $$(1,1), (-1,1), (-1,-1)$$ and $$(1, -1)$$. Let $$S$$ be the region consisting of all points inside the square which are nearer to the origin than to any edge. Sketch the region $$S$$ and find its area.

Questions Asked from Application of Integration (Subjective)

Number in Brackets after Paper Indicates No. of Questions

IIT-JEE 2006 (1)
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