JEE Main 2013 (Offline) | Definite Integrals and Applications of Integrals Question 269 | Mathematics

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

Statement-1 : The value of the integral
$$\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}} $$ is equal to $$\pi /6$$

Statement-2 : $$\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.$$

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

Statement- 1 is true; Statement-2 is False.

Statement-1 is false; Statement-2 is true.

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

-1

The area (in square units) bounded by the curves $$y = \sqrt {x,} 2y - x + 3 = 0,$$ $$x$$-axis, and lying in the first quadrant is :

$$9$$

$$36$$

$$18$$

$${{27} \over 4}$$

AIEEE 2012

MCQ (Single Correct Answer)

-1

The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :

$$20\sqrt 2 $$

$${{10\sqrt 2 } \over 3}$$

$${{20\sqrt 2 } \over 3}$$

$$10\sqrt 2 $$

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

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

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

$$\log 2$$

$$\pi \log 2$$

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