1
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
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
$${\log _e}\left( {{3 \over 4}} \right)$$
2
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
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
$${1 \over e}$$
3
WB JEE 2021
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is
A
72
B
125
C
43
D
69
4
WB JEE 2021
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx} $$. Then
A
I is linear function in 'a'
B
I does not depend on 'a'
C
0 < I < a2 + 1 where I depends on 'a'
D
I is quadratic function in 'a'
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