WB JEE 2009 | Definite Integration Question 13 | Mathematics

WB JEE 2009

MCQ (Single Correct Answer)

-0.25

$$\int\limits_0^{1000} {{e^{x - [x]}}dx} $$ is equal to

$${{{e^{1000}} - 1} \over {e - 1}}$$

$${{{e^{1000}} - 1} \over {1000}}$$

$${{e - 1} \over {1000}}$$

1000 (e $$-$$ 1)

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

The value of the integral $$\int\limits_0^{\pi /2} {{{\sin }^5}xdx} $$ is

$${4 \over {15}}$$

$${8 \over {5}}$$

$${8 \over {15}}$$

$${4 \over {5}}$$

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

If $${d \over {dx}}\{ f(x)\} = g(x)$$, then $$\int\limits_a^b {f(x)g(x)dx} $$ is equal to

$${1 \over 2}[{f^2}(b) - {f^2}(a)]$$

$${1 \over 2}[{g^2}(b) - {g^2}(a)]$$

$$f(b) - f(a)$$

$${1 \over 2}[f({b^2}) - f({a^2})]$$

WB JEE 2010

MCQ (Single Correct Answer)

-0.25

If $${I_1} = \int\limits_0^{3\pi } {f({{\cos }^2}x)dx} $$ and $${I_2} = \int\limits_0^\pi {f({{\cos }^2}x)dx} $$, then

$${I_1} = {I_2}$$

$$3{I_1} = {I_2}$$

$${I_1} = 3{I_2}$$

$${I_1} = 5{I_2}$$

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