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CBSE Questions for Class 12 Commerce Applied Mathematics Definite Integrals Quiz 4 - MCQExams.com

If f(1x)+x2f(x)=0 for x>0, 
and I=x1/xf(z)dz,12x2 
then I is?
  • f(2)f(1/2)
  • f(1/2)f(2)
  • 0
  • None of these
If I1=54e(x+5)2dx and I2=32/31/3e(3x2)2dx 

then I1+I2 equals?
  • 13
  • 13
  • 0
  • None of these
If f(a+x)=f(x) , then a>0,nϵN the value of na0f(x)dx  equals ?
  • (n1)a0f(x)dx
  • (1n)a0f(x)dx
  • na0f(x)dx
  • None of the above
If f(x)=11sinx1+t2dt then f(π3) is
  • nonexistent
  • π/4
  • π3/4
  • none of these
102x+13x16xdx
  • 43log3e16log2e.
  • 43log3e+16log2e.
  • 43log3e13log2e.
  • 23log3e+16log2e.
21(x+1x)3/2x21x2dx
  • 52(52)+852
  • 52(52)852
  • (52)852
  • 32(32)852
Evaluate the integrals balogxxdx
  • 12log(ab)logba
  • 14log(ab)logba
  • log(ab)logba
  • 12log(ab)logba
Given 21ex2dx=a, the value of e4eln(x)dx is?
  • e4e
  • e4a
  • 2e4a
  • 2e4ea
π/20dxsinxequals
  • 0
  • 12
  • 1
  • 3/2
The value of 10dx(x+1)x2+2x is
  • π/6
  • π/3
  • π/2
  • π
Value of π/40(tanxcotx)dx is
  • 2log(21)
  • 2log(2+1)
  • log(2+1)
  • log(21)
The value of balogxxdx is
  • log(ab)log(ba)
  • 12log(ab)log(ba)
  • log(a2b2)
  • (a+b)log(a+b)
If f(x)=Asin(πx2)+B,f(12)=2 and 10f(x)dx=2Aπ
then the constants A and B are
  • A=π2,B=π2
  • A=2π,B=3π
  • A=0,B=4π
  • A=4π,B=0
The value of the integral π/40sinx+cosx3+sin2xdx is
  • log2
  • log3
  • (1/4)log3
  • (1/8)log3
The value of π0dx12αcosx+α2 is
  • π1+α2 if α>1
  • πα21 if α>1
  • π1+α2 if α<1
  • πα21 if α<1
If I=21dx(x+1)x21 then I is equal to
  • 1
  • 1/2
  • 1/2
  • 1/3
The value of 10dxex+ex is
  • tan1e
  • tan1(e)π/4
  • tan1(e)tan1(1/e)
  • tan1(1/e)+π/4
The value of 158dx(x3)x+1 is
  • log53
  • 12log53
  • 2log53
  • 2log(21)
If b>a, and I=baxabxdx, then I equals
  • π2(ba)
  • π(ba)
  • π/2
  • 2π(ba)
Value of 2a0x3/22axdx is
  • 3πa22
  • πa3
  • 2πa3
  • 2πa3
Value of 25014+xdx is
  • 2(291)
  • 2(295)
  • 3291
  • none of these
0f(x+1x)lnxxdx
  • is equal to zero
  • is equal to one
  • is equal to 12
  • can not be evaluated
Ifπ/30cos3+4sinxdx=Klog(3+23)3 then K is
  • 12
  • 13
  • 14
  • 18
Suppose that F(x) is an antiderivative of f(x)=sinxx,x>0 then 31sin2xx can be expressed as
  • F(6)F(2)
  • 12(F(6)F(2))
  • 12(F(3)F(1))
  • 2(F(6)F(2))
If 0<α<1 and I=11dx12αx+α2 then I equals
  • 1/α
  • 2/α
  • 3/α
  • none of these
21/21xsin(x1x)dx has the value equal to 
  • 0
  • 34
  • 54
  • 2
The value of the definite integral 1(ex+1+e3x)1dx is
  • π4e2
  • π4e
  • 1e2(π2tan11e)
  • π2e2
3π10π5sinxsinx+cosxdx is equal to 
  • π
  • π2
  • π4
  • π20
If f(x)=x1lnt1+tdt where x>0, then the value(s) of x satisfying the equation, f(x)+f(1/x)=2 is
  • 2
  • e
  • e2
  • e2
Choose a function f(x) such that it is integrable over every interval on the real line
  • f(x)=[x]
  • f(x)=x|x|
  • f(x)=[sinx]
  • f(x)=|x1|x1
0x(1+x)(1+x2)dx
  • π4
  • π2
  • is sme as 0dx(1+x)(1+x2)
  • cannot be evaluated
State true or false:
The average value of the function f(x) = sin^2xcos^3x on the interval [ -\pi ,\pi ] is 0.
  • True
  • False
I_{1} is equal to
  • \displaystyle \frac {2}{3} \int_{0}^{\pi/2}(sin^{2}\theta)(cos\theta)^{-1/3}d\theta
  • \displaystyle \frac {3}{2} \int_{0}^{\pi/2}(sin^{2}\theta)(cos\theta)^{-1/3}d\theta
  • \displaystyle \frac {2}{3} \int_{0}^{\pi/2}(sin\theta)^{2/3}(cos\theta)^{-1/3}d\theta
  • \displaystyle \frac {3}{2} \int_{0}^{\pi/2}(sin\theta)^{2/3}(cos\theta)^{-1/3}d\theta
Evaluate \displaystyle \int_{0}^{\pi /2} \frac{dx}{2+\sin 2x}
  • \displaystyle \frac{2\pi }{{3}}
  • \displaystyle \frac{\pi }{{3}}
  • \displaystyle \frac{2\pi }{{5}}
  • None of these
  • Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  • Assertion is correct but Reason is incorrect
  • Both Assertion and Reason are incorrect
\displaystyle \int_{\tfrac{1}{\sqrt{3}}}^{0}\dfrac{dx}{\left ( 2x^{2}+1 \right )\sqrt{x^{2}+1}}
  • \displaystyle - \tan^{-1} \dfrac{1}{2}
  • \displaystyle \tan^{-1} 1
  • \displaystyle - \tan^{-1} \dfrac{1}{3}
  • \displaystyle \tan^{-1} \dfrac{1}{\sqrt 2}
The value of definite integral \displaystyle \int_{\infty }^{0}\frac{Ze^{-z}}{\sqrt{1-e^{-2z}}}dz
  • \displaystyle -\frac{\pi }{2}ln2
  • \displaystyle \frac{\pi }{2}ln2
  • \displaystyle -\pi ln2
  • \displaystyle \pi ln\frac{1}{\sqrt{2}}
The derivative of F(x)=\displaystyle\int^{x^3}_{x^2}\frac{dt}{log t}(x >0) is 
  • \displaystyle\frac{1}{3log x}
  • \displaystyle\frac{1}{3log x}-\frac{1}{2log x}
  • (log x)^{-1}x(x-1)
  • \displaystyle\frac{3x^2}{log x}
If \displaystyle \int _{ 0 }^{ 1 }{ { e }^{ { x }^{ 2 } }\left( x-\alpha  \right)  } dx=0, then
  • 1<\alpha <2
  • \alpha <2
  • 0<\alpha<1
  • \alpha=0
Trapezoidal rule for evaluation of \displaystyle\int _{ a }^{ b }{ f(x)dx } requires the interval (a,b) to be divided into
  • 2n sub-intervals of equal width
  • any number of sub intervals of not equal width
  • any number of sub intervals of equal width
  • 3n sub-intervals of equal width
\displaystyle \int _{ 0 }^{ a }{ \frac { dx }{ a+\sqrt { { a }^{ 2 }-{ x }^{ 2 } }  }  } is equal to
  • \displaystyle \frac { \pi  }{ 2 } +1
  • \displaystyle \frac { \pi  }{ 2 } -1
  • \displaystyle 1-\frac { \pi  }{ 2 }
  • none of these
The value of the integral \int_0^{\dfrac{\pi}{2}}\,sin^5x\,dx is
  • \dfrac{4}{15}
  • \dfrac{8}{5}
  • \dfrac{8}{15}
  • \dfrac{4}{5}
Using Trapezoidal rule and following table \int_0^8 {f(x)}dx is equal to 
x02468
f(x)25101726
  • 184
  • 92
  • 46
  • -36
\displaystyle \int_1^{\sqrt 3}\frac {dx}{1+x^2} equals
  • \dfrac {\pi}{3}
  • \dfrac {2\pi}{3}
  • \dfrac {\pi}{6}
  • \dfrac {\pi}{12}
\displaystyle\int _{ 1 }^{ 3 }{ \dfrac { \cos { \left( \log { x }  \right)  }  }{ x } dx } is equal to
  • 1
  • \cos { \left( \log { 3 } \right) }
  • \sin { \left( \log { 3 } \right) }
  • \dfrac { \pi }{ 4 }
The value of I=\displaystyle \int _{ 0 }^{ \frac { \pi  }{ 4 }  }{ \left( \tan ^{ n+1 }{ x }  \right) dx } +\frac { 1 }{ 2 } \int _{ 0 }^{ \frac { \pi  }{ 2 }  }{ \left( \tan ^{ n+1 }{ \left( \frac { x }{ 2 }  \right)  }  \right) dx } is
  • \cfrac{1}{n}
  • \cfrac{n+2}{2n+1}
  • \cfrac{2n-1}{n}
  • \cfrac{2n-3}{3n-2}
What is \displaystyle \int _{ 0 }^{ 1 }{ \cfrac { \tan ^{ -1 }{ x }  }{ 1+{ x }^{ 2 } }  } dx equal to?
  • \cfrac { { \pi }^{ 2 } }{ 8 }
  • \cfrac { { \pi }^{ 2 } }{ 32 }
  • \cfrac { \pi }{ 4 }
  • \cfrac { \pi }{ 8 }
What is \displaystyle\int _{ 1 }^{ 2 }{ \ln { x } dx } equal to?
  • \ln { 2 }
  • 1
  • \ln { \left( \dfrac { 4 }{ e } \right) }
  • \ln { \left( \dfrac { e }{ 4 } \right) }
If \displaystyle \int_{0}^{b} \displaystyle \frac{dx}{1\, +\, x^2}\, =\, \displaystyle \int_{b}^{\infty} \displaystyle \frac{dx}{1\, +\, x^2}, then b =
  • \tan ^{-1}\, \left (\displaystyle \frac{1}{3} \right )
  • \displaystyle \frac{\sqrt 3}{2}
  • \sqrt 3
  • 1
Select and write the most appropriate answer from the given alternatives for question :
If \displaystyle \int^k_0 4x^3dx=16, then the value of k is _____.
  • 1
  • 2
  • 3
  • 4
0:0:2


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Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers