1
WB JEE 2009
MCQ (Single Correct Answer)
+1
-0.25

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

A
$${{{e^{1000}} - 1} \over {e - 1}}$$
B
$${{{e^{1000}} - 1} \over {1000}}$$
C
$${{e - 1} \over {1000}}$$
D
1000 (e $$-$$ 1)
2
WB JEE 2010
MCQ (Single Correct Answer)
+1
-0.25

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

A
$${4 \over {15}}$$
B
$${8 \over {5}}$$
C
$${8 \over {15}}$$
D
$${4 \over {5}}$$
3
WB JEE 2010
MCQ (Single Correct Answer)
+1
-0.25

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

A
$${1 \over 2}[{f^2}(b) - {f^2}(a)]$$
B
$${1 \over 2}[{g^2}(b) - {g^2}(a)]$$
C
$$f(b) - f(a)$$
D
$${1 \over 2}[f({b^2}) - f({a^2})]$$
4
WB JEE 2010
MCQ (Single Correct Answer)
+1
-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

A
$${I_1} = {I_2}$$
B
$$3{I_1} = {I_2}$$
C
$${I_1} = 3{I_2}$$
D
$${I_1} = 5{I_2}$$
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