Integrals Test

Result

Integrals Test - 59

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Weekly Quiz Competition

Question 1
1 / -0

The value of $$\int_{-1}^{3}[tan^{-1}(\frac{x}{x^{2}+1})+tan^{-1}(\frac{x^{2}+1}{x})]dx$$

A
2$$\pi $$

B
$$\pi $$

C
$$\frac{\pi }{2}$$

D
$$\frac{\pi }{4}$$

Solution
Question 2
1 / -0

The value(s) of $$\int _{ 0 }^{ 1 }{ \cfrac { { x }^{ 4 }{ \left( 1-x \right) }^{ 4 } }{ 1+{ x }^{ 2 } } } dx$$ is (are)

A
$$\cfrac{22}{7}-\pi$$

B
$$\cfrac{2}{105}$$

C
$$0$$

D
$$\cfrac{71}{15}-\cfrac{3\pi}{2}$$

Solution
Question 3
1 / -0

Evaluate : $$\int { \cfrac { dx }{ x\cos { x } } } $$

A
$$\ln { x } +\cfrac { { x }^{ 2 } }{ 2 } +\cfrac { { 3x }^{ 3 } }{ 3 } +...$$

B
$$\ln { x } -\cfrac { { x }^{ 2 } }{ 4 } +\cfrac { { 4x }^{ 4 } }{ 16 } +...$$

C
$$\ln { x } +\cfrac { { x }^{ 2 } }{ 4 } +\cfrac { { 5x }^{ 4 } }{ 96 } +...$$

D
$$\ln { x } -\cfrac { { x }^{ 2 } }{ 3 } +\cfrac { { x }^{ 4 } }{ 9 } +...$$

Solution
Question 4
1 / -0

If $$G(x) = \begin{vmatrix}f(x)f(-x) & 0 & x^{4}\\ 3 & f(x) - f(-x) & \cos x\\ x^{4} & 2x & f(x)f(-x)\end{vmatrix}$$, then $$\int_{-2}^{2} x^{4}G(x)dx$$ is equal to

A
$$-1$$

B
$$0$$

C
$$2$$

D
$$1$$

Solution
Question 5
1 / -0

$$\int _{ 0 }^{ 1 }{ \frac { x }{ 1+\sqrt { x } } dx= }$$

A
$$\frac {5}{3}-\log {4}$$

B
$$\frac {5}{3}+\log {4}$$

C
$$\frac {5}{3}\log {4}$$

D
$$\frac {3}{5}-\log {4}$$

Solution
Question 6
1 / -0

If the primitive of $$\frac{1}{{f\left( x \right)}}\,$$ is equal to $$\,{\left\{ {f\left( x \right)} \right\}^2} + c$$,then f(x) is

A
$$x + D$$

B
$$\frac{x}{2} + d$$

C
$$\frac{{{x^2}}}{2} + d$$

D
$${x^2} + d$$

Solution
Question 7
1 / -0

If $$\int \sqrt{\dfrac{x-5}{x-7}}dx=a\sqrt{x^{2}-12x+35+log}|x-6+\sqrt{x^{2}-12x+35}|+C$$ then $$A$$=

A
$$-1$$

B
$$\dfrac{1}{2}$$

C
$$-\dfrac{1}{2}$$

D
$$1$$

Solution
Question 8
1 / -0

Consider $$f ( x ) = \int _ { 0 } ^ { \pi } \frac { \ln ( 1 + x \cos \theta ) } { \cos \theta } d \theta$$
Range of $$f ( x )$$ is

A
$$( 0 , \pi )$$

B
$$\left( 0 , \pi ^ { 2 } \right)$$

C
$$\left( \frac { - \pi } { 2 } , \frac { \pi } { 2 } \right)$$

D
$$\left( \frac { - \pi ^ { 2 } } { 2 } , \frac { \pi ^ { 2 } } { 2 } \right)$$

Solution
Question 9
1 / -0

$$\int _ { 0 } ^ { \pi ^ { 2 } / 4 } \sin \sqrt { x } d x$$ is

A
0

B
1

C
2

D
4

Solution
Question 10
1 / -0

The value of $$\displaystyle \int _{0}^{\pi/2} \log{\sin{x}}dx$$ is

A
$$-\pi \log{2}$$

B
$$\dfrac{-\pi}{2} \log{2}$$

C
$$\pi \log{2}$$

D
0

Solution