1
IIT-JEE 1999
Subjective
+5
-0
Integrate $$\int\limits_0^\pi {{{{e^{\cos x}}} \over {{e^{\cos x}} + {e^{ - \cos x}}}}\,dx.}$$
2
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 $$8x+1=0.$$

3
IIT-JEE 1998
Subjective
+8
-0
Prove that $$\int_0^1 {{{\tan }^{ - 1}}} \,\left( {{1 \over {1 - x + {x^2}}}} \right)dx = 2\int_0^1 {{{\tan }^{ - 1}}} \,x\,dx.$$
Hence or otherwise, evaluate the integral
$$\int_0^1 {{{\tan }^{ - 1}}\left( {1 - x + {x^2}} \right)dx.}$$
4
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 $$x=1.$$
EXAM MAP
Medical
NEET
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12