1
AIEEE 2007
+4
-1
The solution for $$x$$ of the equation $$\int\limits_{\sqrt 2 }^x {{{dt} \over {t\sqrt {{t^2} - 1} }} = {\pi \over 2}}$$ is
A
$${{\sqrt 3 } \over 2}$$
B
$$2\sqrt 2$$
C
$$2$$
D
None
2
AIEEE 2007
+4
-1
Let $$I = \int\limits_0^1 {{{\sin x} \over {\sqrt x }}dx}$$ and $$J = \int\limits_0^1 {{{\cos x} \over {\sqrt x }}dx} .$$ Then which one of the following is true?
A
$$1 > {2 \over 3}$$ and $$J > 2$$
B
$$1 < {2 \over 3}$$ and $$J < 2$$
C
$$1 < {2 \over 3}$$ and $$J > 2$$
D
$$1 > {2 \over 3}$$ and $$J < 2$$
3
AIEEE 2006
+4
-1
$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx}$$ is equal to
A
$$\pi \int\limits_0^\pi {f\left( {\cos x} \right)dx}$$
B
$$\,\pi \int\limits_0^\pi {f\left( {sinx} \right)dx}$$
C
$${\pi \over 2}\int\limits_0^{\pi /2} {f\left( {sinx} \right)dx}$$
D
$$\pi \int\limits_0^{\pi /2} {f\left( {\cos x} \right)dx}$$
4
AIEEE 2006
+4
-1
$$\int\limits_{ - {{3\pi } \over 2}}^{ - {\pi \over 2}} {\left[ {{{\left( {x + \pi } \right)}^3} + {{\cos }^2}\left( {x + 3\pi } \right)} \right]} dx$$ is equal to
A
$${{{\pi ^4}} \over {32}}$$
B
$${{{\pi ^4}} \over {32}} + {\pi \over 2}$$
C
$${\pi \over 2}$$
D
$${\pi \over 4} - 1$$
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