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CBSE Questions for Class 12 Commerce Maths Integrals Quiz 4 - MCQExams.com

The value of π0dx12αcosx+α2 is
  • π1+α2 if α>1
  • πα21 if α>1
  • π1+α2 if α<1
  • πα21 if α<1
Given 21ex2dx=a, the value of e4eln(x)dx is?
  • e4e
  • e4a
  • 2e4a
  • 2e4ea
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)
Value of 2a0x3/22axdx is
  • 3πa22
  • πa3
  • 2πa3
  • 2πa3
The value of balogxxdx is
  • log(ab)log(ba)
  • 12log(ab)log(ba)
  • log(a2b2)
  • (a+b)log(a+b)
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))
The value of 10dxex+ex is
  • tan1e
  • tan1(e)π/4
  • tan1(e)tan1(1/e)
  • tan1(1/e)+π/4
21/21xsin(x1x)dx has the value equal to 
  • 0
  • 34
  • 54
  • 2
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
Solve 132dx5(3x)4
  • 5(5161)
  • 5(5161)
  • 5(516+1)
  • None of these
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)=sin2xcos3x on the interval [π,π] is 0.
  • True
  • False
I1 is equal to
  • 23π/20(sin2θ)(cosθ)1/3dθ
  • 32π/20(sin2θ)(cosθ)1/3dθ
  • 23π/20(sinθ)2/3(cosθ)1/3dθ
  • 32π/20(sinθ)2/3(cosθ)1/3dθ
Evaluate π/20dx2+sin2x
  • 2π3
  • π3
  • 2π5
  • 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
013dx(2x2+1)x2+1
  • tan112
  • tan11
  • tan113
  • tan112
The value of definite integral 0Zez1e2zdz
  • π2ln2
  • π2ln2
  • πln2
  • πln12
If 10ex2(xα)dx=0, then
  • 1<α<2
  • α<2
  • 0<α<1
  • α=0
a0dxa+a2x2 is equal to
  • π2+1
  • π21
  • 1π2
  • none of these
What is 21lnxdx equal to?
  • ln2
  • 1
  • ln(4e)
  • ln(e4)
π011+sinx dx is equal to
  • 1
  • 2
  • 3
  • 4
The value of x/40secx(secx+tanx)2dx is
  • 1+2
  • 11+2
  • 2
  • None of these
If f(x)={2x2+1,x14x21,x>1, then 20f(x)dx is
  • 10
  • 50/3
  • 1/3
  • 47/2
What is 10tan1x1+x2dx equal to ?
  • π4
  • π8
  • π28
  • π232
If dydt=ky and k0, which of the following could be the equation of y?
  • y=kx7
  • y=95ekt
  • y=5+ln k
  • y=(xk)2
  • y=kx
Solve π20sinϕcos5ϕdϕ.
  • 64231
  • 24231
  • 54231
  • None of these
π/202x3sin(x2)dx is equal to
  • 12(1+π4)
  • 12(1π4)
  • 12(π21)
  • 12(1π2)
  • 12(π41)
17sin(x7+10)dx is equal to
  • 17cos(x7+10)+C
  • 17cos(x7+10)+C
  • cos(x7+10)+C
  • 7cos(x7+10)+C
  • cos(x+70)+C
If 10xdx=π412ln2 then the value of definite integral 10tan1(1x+x2)dx equals :
  • ln2
  • π4+ln2
  • π4ln2
  • 2ln2
The value of 108log(1+x)1+x2dx is
  • π2log2
  • πlog2
  • 2πlog2
  • None of these
If 1+sinxf(x)dx=23(1+sinx)3/2+C, then f(x) is equal to
  • cosx
  • sinx
  • tanx
  • 1
π/20f(sin2x)sinxdx=Kπ/20f(cos2x)cosxdx where k equals to
  • 2
  • 4
  • 2
  • 22
10dxxx
  • 2
  • 2
  • 1
  • 3
What is 2π01+sinx2dx equal to?
  • 8
  • 4
  • 2
  • 0
Let I=π/3π/4sinxxdx. Then?
  • 12I1
  • 4I230
  • 38I26
  • 1I232
(ex)x(2+logx)dx=....+c,xR+{1}
  • xx
  • (ex)x
  • ex
  • (1+logx)(ex)x
If I=10x(1x)1/2dx and 60I+k=25 then k= _________. (kR).
  • 9
  • 25
  • 60
  • 41
321dxx1/51+x4/5
  • 25(17+2)
  • 25(172)
  • 52(172)
  • 52(17+2)
π/20sin2x.sinxdx=.....
  • 13
  • 23
  • 23
  • 43
Evaluate 5π2πcot1(tanx)dx.
  • 0
  • 1
  • 1
  • 2
(3.x2.tan1x+x31+x2)dx=....+c.
  • x3tan1x
  • x33tan1x
  • x2tan1x
  • x22tan1x
If π/20sinxcosxdx is equal to:
  • 12
  • 14
  • 2
  • 1
I=x+2(x+1)2dx; then I is equal to 
  • log(x+1)+1x+1+c
  • log(x+2)1x+1+c
  • log(1+x)1x+1+c
  • log(x+2)+1x+1+c
If π/30cosx3+4sinxdx=klog(3+233), then, k is equal to ?
  • 12
  • 13
  • 14
  • 18
Find proper substitution
10ex1+exdx
  • 1+ext
  • exdxdt
  • 10dtt
  • 10ln|t|
0:0:1


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