AIEEE 2011 | Definite Integrals and Applications of Integrals Question 273 | Mathematics

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AIEEE 2011

MCQ (Single Correct Answer)

-1

The value of $$\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$$ is

$${\pi \over 8}\log 2$$

$${\pi \over 2}\log 2$$

$$\log 2$$

$$\pi \log 2$$

AIEEE 2011

MCQ (Single Correct Answer)

-1

The area of the region enclosed by the curves $$y = x,x = e,y = {1 \over x}$$ and the positive $$x$$-axis is

$$1$$ square unit

$${3 \over 2}$$ square units

$${5 \over 2}$$ square units

$${1 \over 2}$$ square unit

AIEEE 2010

MCQ (Single Correct Answer)

-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

$$21$$

$$41$$

$$42$$

$$\sqrt {41} $$

AIEEE 2010

MCQ (Single Correct Answer)

-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

$$4\sqrt 2 + 2$$

$$4\sqrt 2 - 1$$

$$4\sqrt 2 + 1$$

$$4\sqrt 2 - 2$$

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