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

{(logx1)1+(logx)2}2dx is equals to?
  • logx(logx)2+1+C
  • xx2+1+C
  • xex1+x2+C
  • x(logx)2+1+C
The value of the integral ππ(cospxsinqx)2dx where p,q are integers, is equal to:-
  • π
  • 0
  • π
  • 2p
cosx+2sinx7sinx5cosxdx=ax+bln|7sinx5cosx|+c then a+b is
  • 117
  • 337
  • 1337
  • 2347
dxsin2xcos2x equals-
  • tanxcotx+C
  • tanx+cotx+c
  • tanxcotx+c
  • tanxcot2x+c
1x2(1+x2)1+x4dx is equal to 
  • 2sin1{2xx2+1}+c
  • 12sin1{2xx2+1}+c
  • 12sin1{2xx2+1}+c
  • 12sin1{x2+12x}+c
(x+3)ex(x+4)2dx is equal to
  • 1(x+4)2+C
  • ex(x+4)2+C
  • exx+4+C
  • exx+3+C
If x2tan1x1+x2dx=tan1x12log(1+x2)+f(x)+c then f(x)=
  • tan1x2
  • 12(tan1x)2
  • tan1x2
  • None of these
10dx(x2+1)(x2+2)=
  • π4+12tan112
  • π212tan112
  • π412tan112
  • π312tan112
The value of 11cot1xπdx
  • 1
  • 2
  • 3
  • 0
(x6+7x5+6x4+5x3+4x2+3x+1)exdx equals
  • 6j=0xjex+c
  • 7j=1xjex+c
  • 6i=1xiex+c
  • 5i=0xiex+c
The integral a/22a/4(2cosecx)17 dx is equal to:
  • log(1+2)02(eu+eu)16du
  • log(1+2)0(eu+eu)17du
  • log(1+2)0(eueu)17du
  • log(1+2)02(eueu)16du
Evaluate: x2+1x4+1dx equals 
  • 12tan1(x212x)+C
  • 12tan1(1x22x)+C
  • 12tan1(x212x)+C
  • 12tan1(1x22x)+C
Solve:dx(x3)x+1
  • cosh1(1x3(1+x))+c
  • sinh1(1x3(1+x))+c
  • sinh1(1x3(1+x))+c
  • cosh1(1x3(1+x))+c
1x2(1+x2)1+x4dx is equal to 
  • 2sin1{2xx2+1}+c
  • 12sin1{2xx2+1}+c
  • 12sin1{2xx2+1}+c
  • 12sin1{x2+12x}+c
The value of the integral 101x1+x dx is
  • π2+1
  • π21
  • -1
  • 1
x31x3+xdx equal to 
  • xlogx+log(x2+1)tan1x+c
  • xlogx+12log(x2+1)tan1x+c
  • x+logx+12log(x2+1)+tan1x+c
  • x+logx12log(x2+1)tan1x+c
The integral (1+2x2+1x)ex21xdx is equal to
  • (2x1).ex21x+c
  • (2x+1).ex21x+c
  • xex21x+c
  • xex21x+c
ex/2sin(x2+π4)dx is equal to---
  • ex/2sinx/2+c
  • ex/2cosx/2+c
  • 2ex/2sinx/2+c
  • 2ex/2cosx/2+c
ex(1+sinx)1+cosxdx=
  • extanx+c
  • exsec2x2+c
  • extanx2+c
  • 12extanx2+c
1sin3xsin(x+a)dx is equal to
  • 2cosecαcosα+sinαtanx+c
  • 2cosecαcosα+sinαcotx+c
  • cosecαcosα+sinαtanx+c
  • cosecαcosα+sinαtanx+c
For xR, f(x)=|log2sinx| and g(x)=f(f(x)), then 
  • g(0)=cos(log2)
  • g(0)=cos(log2)
  • g is differentible at x=0 and g(0)=sin(log2)
  • g is not differentiable at x=0
Solve:
ex(tan1x+11+x2)dx
  • extan1x+c
  • ex1+x2+c
  • extanx+c
  • None of these
1x+x+1dx is equal to
  • 23[(x+1)3/2x3/2]+C
  • 2x3[x+1x]+C
  • ln[xx+1]+C
  • ln[x+1x]+C
x2x24x+3dx= 
  • log|x24x+3|+c
  • log|(x3)(x1)/+c
  • xlog|x3|2log|x2|+x
  • None
The value of the definite integral
a1dθ1+tanθa2=501πK where  a2=1003π2008 and  a1=π2008 The value of K equalls
  • 2007
  • 2006
  • 2009
  • 2008
If g(x)=xxloge(ex)dx then  g(π) equals
  • πlogeπ
  • ππloge(eπ)
  • ππloge(π)
  • ππ
19x225dx=______+c.
  • 130log|3x+53x5|
  • log|x+3x5|
  • 130log|3x53x+5|
  • log|x3x5|
If I=10dx(1+x)(2+x)x(1x) then I= 
  • 2π
  • π
  • π2
  • π6|31|
e3logex.(x4+1)1dx=_________+C.
  • log(x4+1)
  • 14log(x4+1)
  • log(x4+1)
  • 3(x4+1)3
The integral of x2xx3x2+x1 w.r.t x is 
  • 12log|x2+1|+C
  • 12log|x21|+C
  • log|x2+1|+C
  • log|x21|+C
0:0:2


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