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CBSE Questions for Class 12 Commerce Applied Mathematics Definite Integrals Quiz 9 - MCQExams.com

Let I1=2111+x2dx and I2=211xdx. Then
  • I1>I2
  • I2>I1
  • I1=I2
  • I1>2I2
The value (s) of  10x4(1x)41+x2dx is (are)
  • 227π
  • 2105
  • 0
  • 71153π2
If I=10xdx8+x3 then the smallest interval in which I lies is
  • (0,18)
  • (0,19)
  • (0,110)
  • (0,17)
If In=π40tannxdx 

then 1I2+I4,1I3+I5,1I4+I6 are in?
  • A.P
  • H.P
  • G.P
  • 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 f(x)=x1tan1ttdtR, then the value of f(e2)f(1e2)is 
  • 0
  • π2
  • π
  • 2π
The value(s) of 10x4(1x)41+x2dx is (are)
  • 227π
  • 2105
  • 0
  • 71153π2
If 2f(x)+f(x)=1xsin(x1x), then the value of e1ef(x)dx, is
  • 1
  • 0
  • e
  • 1
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
The tangent to the graph of the function y=f(x) at the point with abscissa x = a forms with the x-axis an angle of π/3 and at the point with abscissa x = b at an angle of π/4, then the value of the integral,
baf(x).f(x)dx is equal to
  • 1
  • 0
  • 3
  • -1
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
Evaluate : 0dx(1+x2)4
  • π32
  • 3π32
  • 5π32
  • 7π32
Let f:RR+ and II=k1kxf(x(1x))dx,I2=k1kf(x(1x))dx where 2k1>0. Then III2 is 
  • 2
  • k
  • 1/2
  • 1
The value of 0logxa2+x2
  • 2πlogaa
  • πloga2a
  • πloga
  • 0
11cot1(x+x31+x4)dx is equal to 
  • 2π
  • π2
  • 0
  • π
π/20sinxlog(sinx)dx=
  • logee
  • loge2
  • loge(e/2)
  • loge(2/e)
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
The value of 1/e1f(x)dx+e1f(x)dx where f(x) is given as logx1+x equals 
  • 0
  • 12
  • 12
  • 1
The value of tanx1/et1+t2dt+cotx1/edtt(1+t2) is
  • 1/2
  • 1
  • π/4
  • none of these
Evaluate : 1212x81x4×[sin1(12x2)+cos1(2x1x2)]dx
  • π[12log2+121+tan11221102]
  • π[12log2+121+tan112+21102]
  • π[12log2121+tan11221102]
  • π[12log2121+tan112+21102]
Solve :-
10dx(x2+1)3/2=

  • 1
  • 12
  • 12
  • 2
Solve:-
10dx(x2+1)3/2
  • 1
  • 2
  • 1/2
  • 12
If I=1/30dx(1+x2)1x2 then I is equal to
  • π/2
  • π/22
  • π/42
  • π/4
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
If In=π/40tannx×sec2xdx, then I1,I2,I3, .......are in
  • A.P.
  • G.P.
  • H.P.
  • none
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
If 3+210x2ex2dx=10ex2dx then the value of β is
  • 1e
  • e
  • 12e
  • 2e
If In=10dx(1+x2)n;nN, then which of the following statements hold good?
  • 2nIn+1=2n+(2n1)In
  • I2=π8+14
  • I2=π814
  • I3=π16548
If x1/2x1/2x1/3dx=Ax65x5/6+32x2/3+Bx+Cx1/3+Dx1/6+E In(x1/61)=k, then A+B+C+D+E=
  • 6
  • 12
  • 18
  • 17
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
Value of 160x1/41+x1/2dx is
  • 83
  • 43tan12
  • 4(23+tan12)
  • 4(23tan12)
The solution of x of the equation x2dttt21=π2 is 
  • 22
  • 2
  • π
  • 2
101ax+bdxis
  • zero
  • logea+bb
  • loge(ax+b)
  • 1aloge(a+bb)
80[t]dt at equals to (where [.] greatest integer function.)
  • 28
  • 11
  • 2
  • 8
If π4<α<π2, value of π/2π/2sin2x1+sin2αsinx is
  • 43tanαsecα
  • 43cotαcosecα
  • 43tanαcosecα
  • 43cotαsecα
If I1=1xdt1+t2 and I2=1/x1dt1+t2 for x>0, then
  • I1=I2
  • I1>I2
  • I2>I1
  • I2=(π/2)tan1x
If I1=0dx1+x4 and I2=0x21+x4dx, then
  • I1=I2
  • I1=2I2
  • 2I1=I2
  • none of these
If 0log(1+x2)1+x2dx=λ10log(1+x)1+x2dx then λ equals
  • 4
  • π
  • 8
  • 2π
0:0:1


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