1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
If $$f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$$ and g(x) = logex, (x > 0) then the value of integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}}$$ is
A
loge3
B
loge2
C
loge1
D
logee
2
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
The area (in sq. units) of the region
A = { (x, y) $$\in$$ R × R|  0 $$\le$$ x $$\le$$ 3, 0 $$\le$$ y $$\le$$ 4, y $$\le$$ x2 + 3x} is :
A
$${{59} \over 6}$$
B
$${{26} \over 3}$$
C
8
D
$${{53} \over 6}$$
3
JEE Main 2019 (Online) 12th January Evening Slot
+4
-1
The integral $$\int\limits_1^e {\left\{ {{{\left( {{x \over e}} \right)}^{2x}} - {{\left( {{e \over x}} \right)}^x}} \right\}} \,$$ loge x dx is equal to :
A
$$- {1 \over 2} + {1 \over e} - {1 \over {2{e^2}}}$$
B
$${3 \over 2} - e - {1 \over {2{e^2}}}$$
C
$${1 \over 2} - e - {1 \over {{e^2}}}$$
D
$${3 \over 2} - {1 \over e} - {1 \over {2{x^2}}}$$
4
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
The area (in sq. units) of the region bounded by the parabola, y = x2 + 2 and the lines, y = x + 1, x = 0 and x = 3, is
A
$${{15} \over 4}$$
B
$${{15} \over 2}$$
C
$${{21} \over 2}$$
D
$${{17} \over 4}$$
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