1
AIEEE 2011
+4
-1
The value of $$\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$$ is
A
$${\pi \over 8}\log 2$$
B
$${\pi \over 2}\log 2$$
C
$$\log 2$$
D
$$\pi \log 2$$
2
AIEEE 2011
+4
-1
The area of the region enclosed by the curves $$y = x,x = e,y = {1 \over x}$$ and the positive $$x$$-axis is
A
$$1$$ square unit
B
$${3 \over 2}$$ square units
C
$${5 \over 2}$$ square units
D
$${1 \over 2}$$ square unit
3
AIEEE 2010
+4
-1
Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x)=p'(1-x),$$ for all $$x \in \left[ {0,1} \right],p\left( 0 \right) = 1$$ and $$p(1)=41.$$ Then $$\int\limits_0^1 {p\left( x \right)dx}$$ equals
A
$$21$$
B
$$41$$
C
$$42$$
D
$$\sqrt {41}$$
4
AIEEE 2010
+4
-1
The area bounded by the curves $$y = \cos x$$ and $$y = \sin x$$ between the ordinates $$x=0$$ and $$x = {{3\pi } \over 2}$$ is
A
$$4\sqrt 2 + 2$$
B
$$4\sqrt 2 - 1$$
C
$$4\sqrt 2 + 1$$
D
$$4\sqrt 2 - 2$$
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