AIEEE 2002 | Definite Integration Question 297 | Mathematics

$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ then $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]$$ equals

$${1 \over 2}$$

$$1$$

$$\infty $$

zero

AIEEE 2002

MCQ (Single Correct Answer)

-1

$$\int\limits_0^2 {\left[ {{x^2}} \right]dx} $$ is

$$2 - \sqrt 2 $$

$$2 + \sqrt 2 $$

$$\,\sqrt 2 - 1$$

$$ - \sqrt 2 - \sqrt 3 + 5$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

$$\int_{ - \pi }^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} dx$$ is

$${{{\pi ^2}} \over 4}$$

$${{\pi ^2}}$$

zero

$${\pi \over 2}$$

AIEEE 2002

MCQ (Single Correct Answer)

-1

If $$y=f(x)$$ makes +$$ve$$ intercept of $$2$$ and $$0$$ unit on $$x$$ and $$y$$ axes and encloses an area of $$3/4$$ square unit with the axes then $$\int\limits_0^2 {xf'\left( x \right)dx} $$ is

$$3/2$$

$$1$$

$$5/4$$

$$-3/4$$

Questions Asked from Definite Integration (MCQ (Single Correct Answer))

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