Integrals Test

Result

Integrals Test - 64

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Weekly Quiz Competition

Question 1
1 / -0

$$\displaystyle \overset{3}{\underset{0}{\int}} \dfrac{dx}{\sqrt{5 - x^2}}$$

A
$$\dfrac{\pi}{6}$$

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

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

D
$$-\dfrac{\pi}{6}$$
Question 2
1 / -0

$$\displaystyle\int _{ 0 }^{ \infty }{ \dfrac { dx }{ \left( x+\sqrt { { x }^{ 2 }+1 } \right) ^{ 3 } } } =$$

A
$$\dfrac{3}{8}$$

B
$$\dfrac{1}{8}$$

C
$$-\dfrac{3}{8}$$

D
$$None\ of\ these$$
Question 3
1 / -0

$$\overset { x }{ \underset { 0 }{ \int } } log(1-cos )$$

A
$$-\pi log2$$

B
$$log2$$

C
$$log 4$$

D
none of these

Solution
Question 4
1 / -0

If I =$$\overset { 2 }{ \underset { -3 }{ \int } } (|x + 1| + |x + 2| +|x -1|) dx$$, then i equals

A
$$\dfrac{31}{2}$$

B
$$\dfrac{35}{2}$$

C
$$\dfrac{47}{2}$$

D
$$\dfrac{39}{2}$$

Solution
Question 5
1 / -0

If $$f(x)\int _{ 1 }^{ x }{ \frac { { tan }^{ 1 }t }{ t } } dt(x>0)$$, then the value of $$f({ o }^{ 2 })-f(\frac { 1 }{ o^{ 2 } } )$$

A
$$\pi $$

B
$$2\pi $$

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

D
0

Solution
Question 6
1 / -0

If $$I=\displaystyle\int _{ 8 }^{ 15 }{ \dfrac { dx }{ \left( x-3 \right) \sqrt { x+1 } } } $$, then $$I$$ equals

A
$$\dfrac{1}{2}\log\dfrac{5}{3}$$

B
$$2\log\dfrac{1}{3}$$

C
$$\dfrac{1}{2}\log\dfrac{1}{5}$$

D
$$2\log\dfrac{5}{3}$$

Solution
Question 7
1 / -0

The floor value of integral $$\displaystyle \int_\dfrac{\pi }{4}^{3\pi }\dfrac{x}{1+4x}dx$$ is

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution
Question 8
1 / -0

Value of $$ \displaystyle \int_{1}^{5} \left(\sqrt {x+2\sqrt {x-1}}+\sqrt {x-2(x-1)}\right)dx$$ is

A
$$\dfrac {8}{3}$$

B
$$\dfrac {16}{3}$$

C
$$\dfrac {32}{3}$$

D
$$\dfrac {34}{3}$$

Solution
Question 9
1 / -0

If $$3+2\displaystyle\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ e }^{ -x^{ 2 } } } dx=\displaystyle\int _{ 0 }^{ 1 }{ { e }^{ -x^{ 2 } } } dx$$ then the value of $$\beta$$ is

A
$$\dfrac{1}{e}$$

B
$$e$$

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

D
$$2e$$
Question 10
1 / -0

If $$a > 0$$ and $$A=\displaystyle \int^{a}_{0}\cos^{-1}xdx$$, then $$\int ^{a}_{-a}(\cos^{-1}x-\sin^{1}\sqrt {1-x^{2}})dx=\pi a-\lambda A$$. Then $$\lambda$$

A
$$0$$

B
$$3$$

C
$$2$$

D
$$none\ of\ these$$

Solution