CBSE Questions for Class 12 Commerce Maths Integrals Quiz 11 - MCQExams.com

What is $$\int _ { 1 } ^ { 3 } \left| 1 - x ^ { 4 } \right| d x$$ equal to $$?$$
  • $$- 232 / 5$$
  • $$- 116 / 5$$
  • $$ 116 / 5$$
  • $$ 232 / 5$$
The value of $$\int _{ 3/2 }^{ 2 }{ { \left( \cfrac { x-1 }{ 3-x }  \right)  }^{ 1/2 } } dx$$ is
  • $$\cfrac { \sqrt { 3 } }{ 2 } -1+\cfrac { \pi }{ 6 } $$
  • $$\cfrac { \sqrt { 3 } }{ 2 } -1+\cfrac { \pi }{ 8 } $$
  • $$\cfrac { \sqrt { 3 } }{ 2 } +1-\cfrac { \pi }{ 6 } $$
  • None of these
The value of integral $$\int _{ a }^{ b }{ \frac { \left| x \right|  }{ x } dx,\quad a<b }$$ is 
  • $$\left| a \right| -\left| b \right|$$
  • $$\left| b \right| -\left| a \right|$$
  • $$\left| a \right| -b$$
  • $$\left| b \right| -a$$
The value of the definite integral $$\int _0^1 (1+e^{-x^2})dx$$ is
  • $$-1$$
  • $$2$$
  • $$1+e^{-1}$$
  • None of the above
Let $$J=\int _{ 0 }^{ \infty  }{ \dfrac { Inx }{ 1+{ x }^{ 3 } }  } dx$$ and $$K=\int _{ 0 }^{ \infty  }{ \dfrac { xInx }{ 1+{ x }^{ 3 } }  } dx$$ then
  • $$J+K=0$$
  • $$J-K=0$$
  • $$J+K<0$$
  • $$J+K>0$$
The integral $$\int^{\pi/3}_{\pi/6} \dfrac{f(x)}{f(x) +f(\dfrac{\pi}{2} -x)} dx$$ is equal to
  • $$\dfrac{\pi}{12}$$
  • $$\dfrac{12}{\pi}$$
  • $$\dfrac{\pi}{13}$$
  • $$\dfrac{13}{\pi}$$
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 $$\lambda$$
  • $$0$$
  • $$3$$
  • $$2$$
  • $$none\ of\ these$$
$$\displaystyle \int_{\pi/4}^{\pi/2}{\sqrt{2+\sqrt{2+2\cos 4x}}dx}$$ is equal to 
  • $$\sqrt{2}$$
  • $$\sqrt{2(\sqrt{2-1})}$$
  • $$2$$
  • $$none\ of\ these$$
$$\int {{{\left( {1 + {x^4}} \right)}^{\dfrac{1}{4}}}dx = A\;In\;\left( {\dfrac{{{{\left( {1 + {x^4}} \right)}^{\dfrac{1}{4}}} + x}}{{{{\left( {1 + {x^4}} \right)}^{\dfrac{1}{4}}} - x}}} \right) + B\;\tan {\;^{ - 1}}\left( {\dfrac{{{{\left( {1 + {x^4}} \right)}^{\dfrac{1}{4}}}}}{x}} \right) + C,\;then\;A + B = } $$
  • 1/4
  • 1/2
  • $$ - \dfrac{1}{4}$$
  • $$ - \dfrac{1}{2}$$
$$\displaystyle \int_{4}^{5}e^{(x + 5)^2} dx +  3\int_{1/3}^{2/3}e^{9\left ( x \dfrac{2}{3} \right )^2}dx$$  is equal to
  • 1
  • -1
  • 0
  • 2
Let $$ 1 _ { n } = \int _ { 0 } ^ { \frac { 1 } { 2 } } \frac { 1 } { \sqrt { 1 - x ^ { n } } } d x $$ where $$ n > 2 , $$ then
  • $$

    I _ { n } < \frac { \pi } { 6 }

    $$
  • $$

    I _ { n } > \frac { \pi } { 6 }

    $$
  • $$

    \mathrm { I } _ { \mathrm { n } } < \frac { 1 } { 2 }

    $$
  • $$

    I _ { n } > \frac { 1 } { 2 }

    $$
If $$\int _{ 0 }^{ b-c }{ f\left( x+c \right) dx=k\int _{ b }^{ c }{ f\left( x \right) dx }  } $$ then k=
  • 0
  • 1
  • 2
  • -1
If $$l_1-\int _{ 0 }^{ 1 }{ { 2 }^{ { x }^{ 2 } } } ,{ l }_{ 2 }-\int _{ 0 }^{ 1 }{ { 2 }^{ { x }^{ 3 } } } dx,{ l }_{ 3 }-\int _{ 1 }^{ 2 }{ { 2 }^{ { x }^{ 2 } } } dx$$ and $$l_4-\int _{ 1 }^{ 2 }{ { 2 }^{ { x }^{ 3 } } } dx$$ then
  • $$l_2 > l_1$$
  • $$l_1 > l_2$$
  • $$l_3-l_2$$
  • None of these
Find the value of the equation :  $$\int _ { \ln \lambda } ^ { \ln \left( \frac { 1 } { \lambda } \right) }  \dfrac { f \left( \dfrac { x ^ { 2 } } { 3 } \right) ( f ( x ) + f ( - x ) ) } { g \left( 3 x ^ { 2 } \right) ( g ( x ) - g ( - x ) ) } d x =?$$   where  $$\lambda > 1$$
  • $$0$$
  • $$1$$
  • $$\lambda$$
  • $$1 / \lambda$$
Find the value of the equation  $$\int _ { 0 } ^ { \infty } \dfrac { d x } { \left( x + \sqrt { x ^ { 2 } + 1 } \right) ^ { 3 } } =?$$
  • $$3 / 8$$
  • $$1/8$$
  • $$-3/8$$
  • $$-1/8$$
$$7 \left( \int_{\pi}^{0}\dfrac{x^{4}(1-x)^{4} dx}{1+x^{2}}+\pi \right)$$ is equal to 
  • $$21$$
  • $$22$$
  • $$23$$
  • $$none\ of\ these$$
$$\int _{ 0 }^{ 1 }{ \sqrt { \cfrac { 1-x }{ 1+x }  } dx } $$, is equal to:
  • $$\cfrac { \pi } { 4 } - 1$$
  • $$\cfrac { \pi } { 2 } - 1$$
  • $$\frac { \pi } { 4 } + 1$$
  • $$\cfrac { \pi } { 2 } + 1$$
$$\int _ { 0 } ^ { 1 } \sqrt { \cfrac { 1 - x } { 1 + x } } d x ,$$ is equal to
  • $$\cfrac { \pi } { 4 } - 1$$
  • $$\cfrac { \pi } { 2 } - 1$$
  • $$\cfrac { \pi } { 4 } + 1$$
  • $$\cfrac { \pi } { 2 } + 1$$
$$\frac { 1 }{ \pi  } \int _{ -2 }^{ 2 }{ \frac { 1 }{ 4+{ x }^{ 2 } } dx= } $$
  • $$0$$
  • $$\frac { 1 }{ 4 } $$
  • $$\frac { \pi }{ 4 } $$
  • $$\frac { 1 }{ 2 } $$
$$\int _{ 0 }^{ 8 }{ \left[ \sqrt { t }  \right]  } dt$$ at equals to (where [.] greatest integer function.)
  • 28
  • 11
  • 2
  • 8
If $$f\left( x \right) =\int _{ 0 }^{ 1 }{ \left( xf\left( t \right) +1 \right) dt,then\int _{ 0 }^{ 3 }{ f\left( x \right) dx=12 }  } $$ 
because 
Statement-2: f(x) = 3x + 1
  • Statements-1 is true, statements-2 is true and statements-2 is correct explanation for statement-1.
  • Statements-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statements-1.
  • Statements-1 is true, statements-2 is false.
  • Statements-1 is false, statements-2 is true.
If $${ I }_{ m }=\overset { e }{ \underset { 1 }{ \int   }  } (lnx)^{ m }dx,$$ where $$m\epsilon N,$$then $${ I }_{ 10 }+10{ I }_{ 9 }$$ is equal to-
  • $${ e }^{ 10 }$$
  • $$\frac { { e }^{ 10 } }{ 10 } $$
  • e
  • e-1
If for every integer n, $$\int _{ n }^{ n+1 }{ f(x)dx={ n }^{ 2 } } $$, then the value of $$\int _{ -2 }^{ 4 }{ f(x)dx } $$ is -
  • 16
  • 14
  • 19
  • None of these.
$$\displaystyle E = \int_{R}^{\infty}\dfrac{GMm}{x^2}$$ dx , (where $$G$$ , $$M$$ , $$m$$ are constants ) equal to
  • $$-\dfrac{GMm}{R^2}$$
  • $$+\dfrac{GMm}{R^2}$$
  • $$-\dfrac{GMm}{R}$$
  • $$+\dfrac{GMm}{R}$$
$$\int _{ 0 }^{ 4036 }{ \dfrac { { 2 }^{ x } }{ { 2 }^{ x }+{ 1 }^{ 4036-x } }  } dx=............$$
  • 2018
  • 4035
  • 2017
  • -2015
If $${ I }_{ 1 }=\int _{ x }^{ 1 }{ \cfrac { 1 }{ 1+{ t }^{ 2 } }  } dt$$ and $${ I }_{ 2 }=\int _{ 1 }^{ 1/x }{ \cfrac { 1 }{ 1+{ t }^{ 2 } }  } dt$$ for x > 0, then 
  • $${ I }_{ 1 }={ I }_{ 2 }$$
  • $${ I }_{ 1 }>{ I }_{ 2 }$$
  • $${ I }_{ 2 }>{ I }_{ 1 }$$
  • None of these.
The value of the integral $$\int _{ \dfrac { 1 }{ 3 }  }^{ 1 }{ \dfrac { \left( x-{ x }^{ 3 } \right) ^{ \dfrac { 1 }{ 3 }  } }{ { x }^{ 4 } }  }dx $$ is
  • 6
  • 0
  • 3
  • 4
$$\overset { -5 }{ \underset { -4 }{ \int }  } e^(x + 5)^2 dx + 3  \overset { 2/3}{ \underset { 1/3 }{ \int }  } e^9(9(x-2/3)^2$$ dx is equal toi 
  • $$e^5$$
  • $$e^4$$
  • $$3e^2$$
  • 0
If $$z=x+3i$$ then value of $$\displaystyle\int^4_2\left[arg\left|\dfrac{z-i}{z+i}\right|\right]dx$$, where $$[.]$$ denotes the greatest integer function, is?
  • $$3\sqrt{2}$$
  • $$6\sqrt{3}$$
  • $$\sqrt{6}$$
  • None
The area of the region bounded by the lines $$x = 1, x = 2$$, and the curves $$x(y - e^x) = \sin x$$ and $$2xy = 2 \sin x + x^3$$ is 
  • $$e^2 - e - \dfrac{1}{6}$$
  • $$e^2 - e - \dfrac{7}{6}$$
  • $$e^2 - e + \dfrac{1}{6}$$
  • $$e^2 - e + \dfrac{7}{6}$$
Suppose $$I_1=\displaystyle \int_{0}^{\pi/2} \cos(\pi \sin^2 x)dx;I_2=\displaystyle \int_{0}^{\pi/2} \cos(2\pi \sin^2x)dx$$ and $$I_3=\displaystyle \int_{0}^{\pi/2} \cos(\pi \sin x)dx $$ then
  • $$I_1=0$$
  • $$I_2+I_3=0$$
  • $$I_1+I_2+I_3=0$$
  • $$I_2=I_3$$
If $$\displaystyle\int \dfrac{\cos x \, dx}{\sin^3x(1+\sin^6x)^{2/3}} = f(x)(1 + \sin^6x)^{1/\alpha} + c$$
Where $$c$$ is a constant of integration, then $$\lambda f\left(\dfrac{\pi}{3}\right)$$ is equal to:
  • $$\dfrac{9}{8}$$
  • $$-2$$
  • $$2$$
  • $$-\dfrac{9}{8}$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers