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CBSE Questions for Class 12 Commerce Applied Mathematics Definite Integrals Quiz 7 - MCQExams.com

π/40log(1+tan2θ+2tanθ)dθ=
  • πlog2
  • (πlog2)/2
  • (πlog2)/4
  • log2
If 2x14xdx=Ksin1(2x)+C, then K is equal to 
  • n2
  • 12n2
  • 12
  • 1n2
The value of the defined integral π/20(sinx+cosx)exsinxdx equals
  • 2eπ/2
  • eπ/2
  • 2eπ/2.cos1
  • 12eπ/4
Evaluate π/20cosx(1+sin2x)dx
  • π2
  • π4
  • π
  • None of these
Evaluate 83x1+x2dx
  • 193
  • 196
  • 383
  • 94
Evaluate π/20cos3xdx
  • 1
  • 34
  • 23
  • None of these
Evaluate : 101x1+xdx
  • π2
  • (π21)
  • (π2+1)
  • None of these
Evaluate: 11/3(xx3)1/3x4dx=
  • 3
  • 0
  • 6
  • 4
Evaluatea0xdxa2+x2
  • a(21)
  • a(12)
  • a(1+2)
  • 2a3
The correct evaluation of π/20sinxsin2x is 
  • 43
  • 13
  • 34
  • 23
ex3+x21(3x4+2x3+2x2x=h(x)+c then the value of h(1)h(1).
  • 1
  • -1
  • 2
  • -2
π0x2(1+sinx)2dx equals
  • π(π2)
  • π2(π2)
  • π(2π)
  • none of these
The value of the integral π/2π/2(x2+logπxπ+x)cosxdx is 
  • 0
  • π224
  • π22+4
  • π22
Let  θ  be the angle between the lines  L1:[x=2t+1y=t+1z=3t+1  and  L2:[x=3s+2y=6s1z=4  where  s,tR.  Then the value of  θ011+tanxdx=
  • π/6
  • π/4
  • π/2
  • π/3
Let I1=10(1x50)100dx and I2=10(1x50)101dx, then I1I2=
  • 50515050
  • 50515049
  • 5150
  • 101100
99log(x+x2+1)dx equal 
  • 2log(92+1)
  • 2log(92+19)
  • 0
  • 2log(9+92+1)
If π30tanθ2ksecθdθ=112,(k>0), then the value of k is :
  • 2
  • 12
  • 4
  • 1
The value of 2π0xsin8xsin8x+cos8xdx is equal to?
  • 2π
  • π2
  • 2π2
  • 4π
If f(ax)=f(x), then a0f(x)dx=0.

  • True
  • False
400π01cos2x
  • 2002
  • 4002
  • 8002
  • none
10sin1xdx=π21
  • True
  • False
Let a function f:RR be defined as f(x)=x+sinx. The value of 2π0f1(x)dx will
  • 2π2
  • 2π22
  • 2π2+2
  • π2
The value of π40tan2θ dθ=
  • π41
  • π4
  • 1π4
  • none of these
10x(x2+1)32dx=........
  • 13
  • 23
  • 32
  • 112
1/20dx(1+x2)1x2 is equal to?
  • 12tan123
  • 22tan1(32)
  • 22tan1(32)
  • 22tan1(32)
1/21ex(2x2)dx(1x)1x2 is equal to
  • e2(3+1)
  • 3e2
  • 3e
  • e3
314xx2+1dx
  • log5
  • 12log5
  • log25
  • log100
If xlog2dxex1=π6,then x is equal to _________.
  • 4
  • in 8
  • in 4
  • None of these
10dxex+ex is equal to?
  • π4tan1(e)
  • tan1(e)π4
  • tan1(e)+π4
  • tan1(e)
If π20cotxcotx+cosecxdx=m(π+n), then mn is equal to?
  • 1
  • 1
  • 12
  • 12
Evaluate : 10dx(1+x+x2)
  • π3
  • π3
  • π33
  • None of these
Evaluateπ/20ex(1+sinx1+cosx)dx
  • 0
  • π4
  • eπ/2
  • (eπ/21)
Evaluate : 202x2dx
  • π
  • 2π
  • π2
  • None of these
Evaluate : 10(1x)(1+x)dx
  • (log2+1)
  • (log21)
  • (2log21)
  • (2log2+1)
Evaluate : 90dx(1+x)
  • (32log2)
  • (3+2log2)
  • (62log4)
  • (6+2log4)
Evaluate : 22|x|dx
  • 4
  • 3.5
  • 2
  • 0
Evaluate 10(1x)(1+x)dx
  • 12log2
  • (2log2+1)
  • (2log21)
  • (12log21)
Evaluate π/60cosxcos2xdx
  • 14
  • 512
  • 13
  • 712
The value of 199π/2π/2(1+cos2x)dx is?
  • 502
  • 1002
  • 1502
  • 2002
Evaluate : 21|x23x+2|dx
  • 16
  • 16
  • 13
  • 23
Given Im=e1(logx)mdx. If ImK+Im2L=e, then the values of K and L are
  • 11m,1m
  • (1m),1m
  • 11m,m(m2)m1
  • mm1,m2
aax|x|dx=?
  • 0
  • 2a
  • 2a33
  • None of these
12|x|2dx=?
  • 3
  • 2.5
  • 1.5
  • None of these
Evaluate : 10|2x1|dx
  • 2
  • 12
  • 1
  • 0
Value of 32dx(1+x3) is?
  • Less than 1
  • Greater than 2
  • Lies between 3 and 4
  • None of these
The value of the definite integral π/20sin5xsinxdx is
  • 0
  • π2
  • π
  • 2π
Evaluate : 12|2x+1|dx
  • 52
  • 72
  • 92
  • 4
The value of the definite integral 42(x(3x)(4+x)(6x) (10x)+sinx)dx equals
  • cos2+cos4
  • cos2cos4
  • sin2+sin4
  • sin2sin4
Let f:RR be a function as f(x)=(x1)(x+2)(x3)(x6)100. If g(x) is a polynomial of degree 3 such that g(x)f(x)dx does not contain any logarithm function and g(2)=10. Then

g(x)f(x)dx, equals
  • tan1(x22)+c
  • tan1(x11)+c
  • tan1(x)+c
  • None of these
If 12(ax25)dx and 5+21(bx+c)dx=0, then 
  • ax2bx+c=0 has atleast one root in (1,2)
  • ax2bx+c=0 has atleast one root in (-2,-1)
  • ax2+bx+c=0 has atleast one root in (-2,-1)
  • None of the above
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