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CBSE Questions for Class 12 Commerce Applied Mathematics Definite Integrals Quiz 5 - MCQExams.com

π011+sinx dx is equal to
  • 1
  • 2
  • 3
  • 4
If f(x)={2x2+1,x14x21,x>1, then 20f(x)dx is
  • 10
  • 50/3
  • 1/3
  • 47/2
What is 10tan1x1+x2dx equal to ?
  • π4
  • π8
  • π28
  • π232
If In=π/40tannθdθ, where n is a positive integer, then n(In1+In+1) is equal to
  • 1
  • n - 1
  • 1n1
  • None of these
The value of (an1)/n1/nxax+xdx is equal to
  • a2
  • na+22n
  • na22n
  • na2
The value of π0dx5+3cosx is
  • π4
  • π8
  • π2
  • Zero
If xlog21ex1dx=π6, then the value of x is 
  • log2
  • log3
  • log4
  • None of these
π/2π/2cosx ln (1+x1x)dx is equal to.
  • 0
  • π24(1+π2)
  • 1
  • π22
π/202x3sin(x2)dx is equal to
  • 12(1+π4)
  • 12(1π4)
  • 12(π21)
  • 12(1π2)
  • 12(π41)
The value of x/40secx(secx+tanx)2dx is
  • 1+2
  • 11+2
  • 2
  • None of these
If f(x) is defined [2,2] by f(x)=4x23x+1 and g(x)=f(x)f(x)x2+3, then 22g(x)dx is equal to
  • 64
  • 48
  • 0
  • 24
If π0x2(1+sinx)2dx=A the π02x2cos2(x/2)(1+sinx)2dx= ?
  • A+ππ2
  • Aπ+π2
  • Aππ2
  • A+2ππ2
If I=π1/π1xsin(x1x)dx, then I is equal to
  • 0
  • π
  • π1π
  • π+1π
Evaluate 41xxdx
  • 12.8
  • 12.4
  • 7
  • None of these
The value of the definite integral 1(ex+1+e3x)1dx is
  • π4e2
  • π4e
  • 1e2(π2tan11e)
  • π2e2
π/201a+bcosxdx,a>|b|=.
  • 2a2b2tan1a+bab
  • 2a2b2cot1aba+b
  • 2a2b2tan1aba+b
  • πa2b2.
Solve π20sinϕcos5ϕdϕ.
  • 64231
  • 24231
  • 54231
  • None of these
If 10xdx=π412ln2 then the value of definite integral 10tan1(1x+x2)dx equals :
  • ln2
  • π4+ln2
  • π4ln2
  • 2ln2
0xlnx(1+x2)2dx=
  • 1
  • 1
  • 0
  • π2
Given 21ex2dx=a the the value of e4elnxdx is
  • 2e4ea
  • e4a
  • 2e4a
  • e4e
If π2<t<2π3 and =sin2t0dx4cos2tx2 then the value of 2005(I+t)π equals
  • 2004
  • 2006
  • 2005
  • None of these
The function 
f(x)=x1[2(t1)(t2)3+3(t1)2(t2)2]dt has :
  • Maximum at x=1
  • Minimum at x=75
  • Neither maximum nor minimum at x=2
  • All of these
Let f(x) and g(x) be two function satisfying f(x^2)+g (4-x)=4x^3, g(4-x)+g(x)=0, then the value of \int_{-4}^{4} f(x^2)dx is:
  • 512
  • 64
  • 256
  • 0
\int_{0}^{1}{\frac{dx}{x\sqrt{x}}}
  • 2
  • -2
  • 1
  • 3
The value of \displaystyle \int _{ 0 }^{ \dfrac { \pi  }{ 4 }  }{ \cos ^{ 3 }{ 2x } dx } is:
  • \cfrac { 2 }{ 3 }
  • \cfrac { 1 }{ 3 }
  • 0
  • \cfrac { 2\pi }{ 3 }
\int _{ 0 }^{ 1 }{ x{ \left[ 1-x \right]  }^{ 11 } } dx=........
  • -\cfrac { 1 }{ 132 }
  • -\cfrac { 1 }{ 156 }
  • -\cfrac { 1 }{ 121 }
  • -\cfrac { 1 }{ 12 }
What is \displaystyle \int_{0}^{2\pi}\sqrt {1 + \sin \dfrac {x}{2}}dx equal to?
  • 8
  • 4
  • 2
  • 0
The value of \displaystyle \int_{0}^{\dfrac {\pi}{4}} (\sqrt {\tan x} +  \sqrt {\cot x})\,\, dx is equal to
  • \dfrac {\pi}{2}
  • -\dfrac {\pi}{2}
  • \dfrac {\pi}{\sqrt {2}}
  • -\dfrac {\pi}{\sqrt {2}}
\int _{ a }^{ b }{ \cfrac { \log { x }  }{ x }  } dx=.......\quad (where a,b\in { R }^{ + })
  • \cfrac { 1 }{ 2 } \log { \left( ab \right) } \log { \left( \cfrac { b }{ a } \right) }
  • \cfrac { 1 }{ 2 } \log { \left( ab \right) }
  • \log { \left( \cfrac { b }{ a } \right) }
  • 2\log { \left( \cfrac { b }{ a } \right) }
\int _{ 0 }^{ \pi /2 }{ \cfrac { \cos { 2x }  }{ { \left( \sin { x } +\cos { x }  \right)  }^{ 2 } }  } dx=......
  • \cfrac { \pi }{ 4 }
  • \cfrac { \pi }{ 2 }
  • 0
  • -\cfrac { \pi }{ 4 }
Evaluate : \displaystyle\int^1_0\dfrac{dx}{\sqrt{5x+3}}
  • \dfrac{2}{5}(\sqrt{8}-\sqrt{3})
  • \dfrac{2}{5}(\sqrt{8}+\sqrt{3})
  • \dfrac{2}{5}\sqrt{8}
  • None of these
Evaluate : \displaystyle\int^2_0\sqrt{6x+4}dx
  • \dfrac{64}{9}
  • 7
  • \dfrac{56}{9}
  • \dfrac{60}{9}
Evaluate \displaystyle\int^{\pi/4}_0\tan^2xdx
  • \left(1-\dfrac{\pi}{4}\right)
  • \left(1+\dfrac{\pi}{4}\right)
  • \left(1-\dfrac{\pi}{2}\right)
  • \left(1+\dfrac{\pi}{2}\right)
Solve: \displaystyle \int _{ 0 }^{ \pi /4 }{ \tan ^{ 100 }{ x }  } dx+\int _{ 0 }^{ \pi /4 }{ \tan ^{ 102 }{ x }  } dx=....
  • \cfrac { 1 }{ 101 }
  • \cfrac { 1 }{ 102 }
  • \cfrac { 1 }{ 100 }
  • 101
If I=\displaystyle\overset{1}{\underset{0}{\displaystyle\int}}x(1-x)^{1/2}dx and 60I+k=25 then k= _________. (k\in R).
  • 9
  • 25
  • 60
  • 41
\displaystyle \int_1^{32}\dfrac{dx}{x^{1/5}\sqrt{1+x^{4/5}}}
  • \dfrac{2}{5}(\sqrt{17}+\sqrt{2})
  • \dfrac{2}{5}(\sqrt{17}-\sqrt{2})
  • \dfrac{5}{2}(\sqrt{17}-\sqrt{2})
  • \dfrac{5}{2}(\sqrt{17}+\sqrt{2})
\int _{ 0 }^{ 5 }{ \sqrt { 25-{ x }^{ 2 } }  } dx=.........
  • 25\pi
  • \cfrac { 25\pi }{ 4 }
  • \cfrac { \pi }{ 4 }
  • \cfrac { 25 }{ 4 }
\int _{ 0 }^{ \pi /2 }{ \sin { 2x } .\sin { x }  } dx=.....
  • \cfrac{1}{3}
  • \cfrac{2}{3}
  • -\cfrac{2}{3}
  • \cfrac{4}{3}
Evaluate \displaystyle \int_{-2\pi}^{5\pi} \cot^{-1} (\tan x) dx.
  • 0
  • -1
  • 1
  • 2
If \int _{ 0 }^{ \pi /3 }{ \dfrac { \cos { x }  }{ 3+4\sin { x }  } dx } =k\log { \left( \dfrac { 3+2\sqrt { 3 }  }{ 3 }  \right)  }, then, k is equal to ?
  • \dfrac{1}{2}
  • \dfrac{1}{3}
  • \dfrac{1}{4}
  • \dfrac{1}{8}
Find proper substitution
\int _{ 0 }^{ 1 }{ \dfrac { { e }^{ -x } }{ 1+{ e }^{ -x } } dx }
  • 1+{ e }^{ -x }\rightarrow t
  • -{ e }^{ -x }dx\rightarrow dt
  • -\int _{ 0 }^{ 1 }{ \dfrac { dt }{ t } }
  • -\int _{ 0 }^{ 1 }{ ln\left| t \right| }
If \displaystyle  \int _{ 2 }^{ x }{ { \left( { e }^{ x }-1 \right)  }^{ -1 }dx=\left( \dfrac { 3 }{ 2 }  \right)  } then x=
  • \ln 4
  • 1
  • {e}^{2}
  • \dfrac{1}{e}
Integrate \displaystyle \int _{ 0 }^{ 2\pi  }{ \sqrt {1+\sin x }}dx
  • 4
  • 6
  • 8
  • None of these
Evaluate the following integral \int _{ 0 }^{ \infty  }{ \dfrac { dx }{ \left( { x }^{ 2 }+{ a }^{ 2 } \right) \left( { x }^{ 2 }+{ b }^{ 2 } \right)  }  } =
  • \dfrac {\pi (a+b)}{ab}
  • \dfrac {\pi ab}{(a+b)}
  • \dfrac {\pi}{2(a+b)}
  • \dfrac {\pi}{2ab(a+b)}
If \displaystyle \int_{0}^{40} \dfrac{dx}{2x+1} =\log a, then a is:
  • 3
  • 9
  • 81
  • 40
\displaystyle \int_{2}^{4} \dfrac{\sqrt{x^{2}-4}}{x^{4}}dx=
  • \dfrac{3}{32}
  • \dfrac{\sqrt{3}}{32}
  • \dfrac{3}{8}
  • \dfrac{\sqrt{3}}{8}
Integrate \int_{0}^{1}\dfrac{\sqrt x}{1+x^3}
  • \dfrac {\pi}{4}
  • \dfrac {\pi}{3}
  • \dfrac {\pi}{6}
  • \dfrac {\pi}{2}
The value of \displaystyle \int _0^{\pi/2} \sin x \cos x dx

  • \dfrac 12
  • \dfrac 34
  • 2
  • None\ of\ these
\displaystyle \int _{ 0 }^{ 2x }{ \sqrt { 1+\sin { x }  }  } dx
  • \sin\dfrac{x}{2}-\cos\dfrac{x}{2}-\dfrac{\pi}{2}+C
  • \sin\dfrac{x}{2}-\cos\dfrac{x}{2}+\dfrac{\pi}{2}+C
  • 2\sin x - 2\cos x + 2
  • None of these
\displaystyle \int_{0}^{1}{\dfrac{ln(1+x)}{1+{x}^{2}}}dx=
  • \dfrac{\pi}{4}ln{2}
  • \dfrac{\pi}{2}ln{2}
  • \dfrac{\pi}{8}ln{2}
  • \pi\ ln{2}
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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers