1
WB JEE 2022
+2
-0.5

If I is the greatest of $${I_1} = \int\limits_0^1 {{e^{ - x}}{{\cos }^2}x\,dx}$$, $${I_2} = \int\limits_0^1 {{e^{ - {x^2}}}{{\cos }^2}x\,dx}$$, $${I_3} = \int\limits_0^1 {{e^{ - {x^2}}}dx}$$, $${I_4} = \int\limits_0^1 {{e^{ - {x^2}/2}}dx}$$, then

A
I = I1
B
I = I2
C
I = I3
D
I = I4
2
WB JEE 2021
+1
-0.25
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx}$$ is equal to
A
$$1 + {4 \over 3}{\log _e}3$$
B
$$1 + {3 \over 4}{\log _e}3$$
C
$$1 - {4 \over 3}{\log _e}3$$
D
$$1 - {3 \over 4}{\log _e}3$$
3
WB JEE 2021
+1
-0.25
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right\}}^{1/2}}} dx$$ is equal to
A
$${\log _e}\left( {{4 \over 3}} \right)$$
B
$$4\,{\log _e}\left( {{3 \over 4}} \right)$$
C
$$4\,{\log _e}\left( {{4 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 4}} \right)$$
4
WB JEE 2021
+1
-0.25
If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}}$$, then the value of x is
A
1
B
e2
C
log 4
D
$${1 \over e}$$
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