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CBSE Questions for Class 12 Commerce Maths Integrals Quiz 8 - MCQExams.com

552(25x2)3x4dx is equal to
  • π6
  • 2π3
  • 5π6
  • π3
The minimum value of the function f(x) = x0dθcosθ+π/2xdθsinθ where x[0,π2], is  
  • 2ln(2+1)
  • ln(22+2)
  • ln(3+2)
  • ln(2+3)
If 10tan1xxdx  is equal to
  • π20sinxxdx
  • π20xsinxdx
  • 12π20sinxxdx
  • 12π20xsinxdx
The value of the integral log50exex1ex+3dx is
  • 3+2π
  • 4π
  • 2+π
  • none of these
The value of the integral  130dx(1+x2)1x2
  • π22
  • π42
  • π82
  • none of these
Let  I1=10exdx1+x and I2=10x2dxex3(2x3).
Then I1I2 is equal to?
  • 3e
  • e3
  • 3e
  • 13e
The value of 0dx1+x4 is
  • same as that of 0x2+1dx1+x4
  • π22
  • same as that of 0x2dx1+x4
  • π2
Evaluate π40sinx+cosx9+16{1(sinxcosx)2}dx
  • 120(log3)
  • 110(log3)
  • 120(log3)
  • 120(log3log2)
If 2f(x)+f(x)=1xsin(x1x), then the value of e1ef(x)dx, is
  • 1
  • 0
  • e
  • 1
Let I1=2111+x2dx and I2=211xdx. Then
  • I1>I2
  • I2>I1
  • I1=I2
  • I1>2I2
Let ddx(F(x))=esinxx, x>0. If 412esinx2xdx=F(k)F(1), then the possible value of k is
  • 10
  • 14
  • 16
  • 18
The evaluation of pXp+2q1qXq1X2p+2q+2Xp+q+1dx is 
  • XpXp+q+1+C
  • XqXp+q+1+C
  • XqXp+q+1+C
  • XpXp+q+1+C
Let df(x)dx=esinxx,x>0. If 413esinx3xdx=f(k)f(1) then one of the possible values of k is
  • 16
  • 63
  • 64
  • 15
e371πsin(πlogex)xdx is equal to
  • 2
  • 2
  • 2/π
  • 2π
202+x2xdx is equal to
  • π+1
  • 1+π/2
  • π+3/2
  • none of these
0f(x+1x).lnxxdx is equal to
  • 0
  • 1
  • 12
  • cannot be evaluated
1log(t1)t2logt+log(tt1)dt equals
  • 12
  • 13
  • 23
  • None of these
If It=π20sin2txsin2xdx then ,I1,I2,I3 are in
  • A.P.
  • H.P.
  • G.P.
  • None of these
The value of π/20sinθlog(sinθ)dθ equals
  • loge(1e)
  • log2e
  • loge21
  • loge(e2)
If I=π1/π1xsin(x1x)dx then I is equal to
  • 0
  • π
  • π1π
  • π+1π
If x satisfies the equation (10dtt2+2tcosα+1)x2(33t2sin2tt2+1dt)x2=0 
for (0<α<π)
then the value of x is?
  • ±α2sinα
  • ±2sinαα
  • ±αsinα
  • ±2sinαα
Let F(x)=f(x)+f(1x) where f(x)=x1logt1+tdt 
Then F(e) is equal to?
  • 1
  • 2
  • 1/2
  • 0
The value of π/20dθ5+3cosθ is?
  • tan112
  • tan113
  • 12tan112
  • 13tan113
011+xndx,n>1 is equal to?
  • 2011+xdx
  • 11+xndx
  • 1dx(xn1)1/n
  • 101(1xn)1/n
If I1=π/20xsinxdx and I2=π/20tan1xxdx, then I1I2= 

  • 12
  • 1
  • 2
  • π2
If11g(x)1+t2dt=f(x),where,g(x)=sinx , then f(π3) equals

  • π4
  • does not exist
  • π34
  • None of these
If In=π40tannxdx 

then 1I2+I4,1I3+I5,1I4+I6 are in?
  • A.P
  • H.P
  • G.P
  • None of these
a0x4(a2x2)1/2dx equals
  • πa532
  • πa632
  • πa232
  • None of these
The value of tanx1/et1+t2dt+cotx1/edtt(1+t2) is
  • 1/2
  • 1
  • π/4
  • none of these
π/20sinxlog(sinx)dx=
  • logee
  • loge2
  • loge(e/2)
  • loge(2/e)
Evaluate : 1212x81x4×[sin1(12x2)+cos1(2x1x2)]dx
  • π[12log2+121+tan11221102]
  • π[12log2+121+tan112+21102]
  • π[12log2121+tan11221102]
  • π[12log2121+tan112+21102]
If xlog2dxex1=π6, the value of x is
  • 4
  • log8
  • log4
  • none of these
π/30cosθ3+4sinθdθ=λlog3+233 then λ equals
  • 12
  • 13
  • 14
  • 18
The value of tanx1/etdt1+t2+cotx1/edtt(1+t2) is
  • 12+tan2x
  • 1
  • π/4
  • 2π11dt1+t2
The value of the integral βαdx(xα)(βx) for β>α, is
  • sin1α/β
  • π/2
  • sin1β/2α
  • π
π/4π/6dxsin2xis equal to
  • 12log(1)
  • log(1)
  • log3
  • 12log3
Value of 10dx(1+x2)1x2 is?
  • π22
  • π2
  • 2π
  • 22π
The value of 11/2dxx3x2+2x1 is?
  • π/2
  • π/3
  • π/6
  • π/2
If I=1x22x3x21dx, then I equals
  • 1
  • 0
  • π/2
  • π3
If 0<α<π/2 then the value of α0dx1cosxcosα is
  • π/α
  • π/2sinα
  • π/2cosα
  • π/2α
Value of adxx4a2+x2 is
  • 2+23a4
  • 223a2
  • 223a4
  • 2+13a2
The value of 54e(x+5)2dx+32/31/3e9(x2/3)2dx is
  • 2/5
  • 1/5
  • 1/2
  • none of these
If \displaystyle \int _{ 0 }^{ 1 }{ \frac { \sin { t }  }{ 1+t } dt } =\alpha , then the value of the integral \displaystyle \int _{ 4\pi -2 }^{ 4\pi  }{ \frac { \sin { t/2 }  }{ 4\pi +2-t } dt } in terms of \alpha is given by
  • 2\alpha
  • -2\alpha
  • \alpha
  • -\alpha
Value of \displaystyle \int_{0}^{16}\displaystyle \frac{x^{1/4}}{1+x^{1/2}}\: dx is
  • \displaystyle \frac{8}{3}
  • \displaystyle \frac{4}{3}\tan ^{-1}\: 2
  • 4\displaystyle \left ( \displaystyle \frac{2}{3}+\tan ^{-1}\: 2 \right )
  • 4\displaystyle \left ( \displaystyle \frac{2}{3}-\tan ^{-1}\: 2 \right )
If I_{1}= \displaystyle \int_{x}^{1}\displaystyle \frac{dt}{1+t^{2}} and I_{2}= \displaystyle \int_{1}^{1/x}\displaystyle \frac{dt}{1+t^{2}} for x> 0, then
  • I_{1}= I_{2}
  • I_{1}> I_{2}
  • I_{2}> I_{1}
  • I_{2}= \left ( \pi /2 \right )-\tan ^{-1}x
If I_{1}= \displaystyle \int_{0}^{\infty }\displaystyle \frac{dx}{1+x^{4}} and I_{2}= \displaystyle \int_{0}^{\infty }\displaystyle \frac{x^{2}}{1+x^{4}}\: dx, then
  • I_{1}= I_{2}
  • I_{1}=2 I_{2}
  • 2I_{1}= I_{2}
  • none of these
If \displaystyle \int_{0}^{\infty }\displaystyle \frac{\log \left ( 1+x^{2} \right )}{1+x^{2}}\: dx= \lambda \displaystyle \int_{0}^{1}\displaystyle \frac{\log \left ( 1+x \right )}{1+x^{2}}\: dx then \lambda  equals
  • 4
  • \pi
  • 8
  • 2\pi
 If \displaystyle I=\int _{8}^{15} \frac{dx}{(x-3)\sqrt{x+1} } then I equals
  • \displaystyle \frac{1}{2}\log \frac {5}{3}
  • \displaystyle 2 \log \frac{1}{3}
  • \displaystyle \frac{1}{2}-\log \frac {1}{5}
  • \displaystyle 2 \log \frac{5}{3}
37 If n > 1, and \displaystyle I=\int _{0}^{\infty} \frac{dx}{(x+\sqrt{1+x^{2}})^{n}} then I  equals
  • \displaystyle \frac{n}{n^{2}-1}
  • \displaystyle \frac{2n}{n^{2}-1}
  • \displaystyle \frac{n}{2(n^{2}-1)}
  • \displaystyle \sqrt{ n^{2}-1}
A function f is defined by \displaystyle f(x)=\frac{1}{2^{r-1}},\frac{1}{2r}<x\leq \frac{1}{2^{r-1}},r=1,2,3,..... then the value of \displaystyle \int _{0}^{1}f(x)dx is equal
  • \cfrac 13
  • \cfrac 14
  • \cfrac 23
  • \cfrac 12
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