1
JEE Main 2023 (Online) 25th January Evening Shift
+4
-1

The integral $$16\int\limits_1^2 {{{dx} \over {{x^3}{{\left( {{x^2} + 2} \right)}^2}}}}$$ is equal to

A
$${{11} \over {12}} + {\log _e}4$$
B
$${{11} \over 6} + {\log _e}4$$
C
$${{11} \over {12}} - {\log _e}4$$
D
$${{11} \over 6} - {\log _e}4$$
2
JEE Main 2023 (Online) 25th January Morning Shift
+4
-1

The minimum value of the function $$f(x) = \int\limits_0^2 {{e^{|x - t|}}dt}$$ is :

A
2
B
$$2(e-1)$$
C
$$e(e-1)$$
D
$$2e-1$$
3
JEE Main 2023 (Online) 24th January Evening Shift
+4
-1

$$\int\limits_{{{3\sqrt 2 } \over 4}}^{{{3\sqrt 3 } \over 4}} {{{48} \over {\sqrt {9 - 4{x^2}} }}dx}$$ is equal to :

A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$${\pi \over 6}$$
D
$$2\pi$$
4
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

If $$[t]$$ denotes the greatest integer $$\leq t$$, then the value of $$\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] \mathrm{d} x$$ is :

A
$$\frac{\sqrt{37}+\sqrt{13}-4}{6}$$
B
$$\frac{\sqrt{37}-\sqrt{13}-4}{6}$$
C
$$\frac{-\sqrt{37}-\sqrt{13}+4}{6}$$
D
$$\frac{-\sqrt{37}+\sqrt{13}+4}{6}$$
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