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All questions of Integral Calculus for Mathematics Exam
x dx is equal to- a)8/15
- b)4/15
- c)1/5
- d)0
Correct answer is option 'D'. Can you explain this answer?
x dx is equal toa)
8/15
b)
4/15
c)
1/5
d)
0
|
Sakshi Jain answered |
Sinx is an odd function so from property of integration( i.e when limit is from -a to a) so its value is zero
dt, then the derivative of f(x) with respect to x is:- a)
- b)
- c)
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
dt, then the derivative of f(x) with respect to x is:a)
b)
c)
d)
None of these
|
Vaani Jain answered |
Apply Leibniz's rule for differentiation under the integral sign,
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
a)
b)
c)
d)
|
Saurabh Kumar answered |
B) put n= 2 then solve
equals:
is equal to
The moment of inertia of a hollow sphere about a diameter is:
- a)Ma2
- b)
- c)
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
The moment of inertia of a hollow sphere about a diameter is:
a)
Ma2
b)
c)
d)
None of these
|
Veda Institute answered |
Moment of Inertia of a Hollow Sphere about the Diameter
Suppose the mass of a hollow sphere is M, ρ is the density, inner radius R2 and outer radius R1,
∴ M = 4/3π(R13 − R23)ρ
Moment of inertia of a hollow sphere (I) = Moment of inertia of a solid sphere of radius R1 - Moment of inertia of a solid sphere of radius R2
is equal to:
The value of 
- a)25/33
- b)32/231
- c)64/231
- d)28/33
Correct answer is option 'C'. Can you explain this answer?
The value of
a)
25/33
b)
32/231
c)
64/231
d)
28/33
|
|
Veda Institute answered |
Put sin x = t
=> cos x dx = dt
is equal to 
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
a)
b)
c)
d)
|
|
Arghya answered |
Let us assume that 
Therefor
Therefor
xF(sin X) dx is equal to- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
xF(sin X) dx is equal toa)
b)
c)
d)
|
Chirag Verma answered |
...(i)
...(ii)Adding (i) and (ii), we get
Hence
The intrinsic equation of the curve p = r sin α is given by: - a)
- b)
- c)
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
The intrinsic equation of the curve p = r sin α is given by:
a)
b)
c)
d)
None of these
|
|
Veda Institute answered |
Given curve is p = r sin α ....(i)
Hence
or,
Hence
or,
The length of the arc of the parabola x2 = 4ay from the vertex to the extremity of the latus rectum is given by:- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
The length of the arc of the parabola x2 = 4ay from the vertex to the extremity of the latus rectum is given by:
a)
b)
c)
d)
|
|
Veda Institute answered |
Given curve is x2 = 4ay
Differentiating, w.r. to y, we get
implies
implies
Hence Length of the arc between vertex and extremity of latus rectum
Differentiating, w.r. to y, we get
implies
implies
Hence Length of the arc between vertex and extremity of latus rectum
sec x(1 + tan x) dx is equal to
x sec2 (x2 +1) tan (x2 +1) dx is equal to
is equal to
- a)log (ex - e-x)
- b)log (ex + e-x)
- c)log (e-x - ex)
- d)
Correct answer is option 'A'. Can you explain this answer?
a)
log (ex - e-x)
b)
log (ex + e-x)
c)
log (e-x - ex)
d)
|
Satish Sangwan answered |
Let e^x-e^-x=t
e^x+e^-xdx=dt
integration of 1/tdt
logt=put let value then
log(e^x-e^-x)
e^x+e^-xdx=dt
integration of 1/tdt
logt=put let value then
log(e^x-e^-x)
is equal to:- a)
- b)
- c)
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
is equal to:a)
b)
c)
d)
None of these
|
Abhra Chatterjee answered |
The answer is π/8 log 2
is equal to
is equal to:
log tan xdx is equal to:- a)
- b)
- c)
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
log tan xdx is equal to:a)
b)
c)
d)
None of these
|
|
Chirag Verma answered |
... (i)
... (ii)Adding (i) and (ii), we get
Hence,
= K, then the value of 
- a)
- b)2K
- c)
- d)0
Correct answer is option 'B'. Can you explain this answer?
= K, then the value of a)
b)
2K
c)
d)
0
|
|
Diksha Pandey answered |
Use general properties of definite integrals.
The area bounded by the curve y = x3, x -axis and the line x = 1 and x = 4 is given by:- a)128
- b)255/4
- c)127/4
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The area bounded by the curve y = x3, x -axis and the line x = 1 and x = 4 is given by:
a)
128
b)
255/4
c)
127/4
d)
None of these
|
|
Chirag Verma answered |
Given curve is y = x3
The required area = Area ABCD =
The required area = Area ABCD =
, x ≠ 0, then 
- a)4
- b)2
- c)1
- d)0
Correct answer is option 'D'. Can you explain this answer?
a)
4
b)
2
c)
1
d)
0
|
|
Chirag Verma answered |
...(i)
....(ii)Adding (i) and (ii), we get
2l=0
implies 1 = 0
= where [ ] represents greatest integer: 
mπ, then the value of m is: 
The value of the integral 
| sin x | dx is equal to:- a)100
- b)1
- c)200
- d)100π
Correct answer is option 'C'. Can you explain this answer?
The value of the integral | sin x | dx is equal to:
| sin x | dx is equal to:a)
100
b)
1
c)
200
d)
100π
|
|
Veda Institute answered |
[Since sin x is periodic with period π]
The area bounded by the curves y = ex, y = e-x and the line x = 1, is: - a)e + e-1
- b)e + e-1 -1
- c)e - e-1 -1
- d)e + e-1 -2
Correct answer is option 'D'. Can you explain this answer?
The area bounded by the curves y = ex, y = e-x and the line x = 1, is:
a)
e + e-1
b)
e + e-1 -1
c)
e - e-1 -1
d)
e + e-1 -2
|
|
Veda Institute answered |
Given curves are
y = ex
y = e-x
From eqn (i) and (ii), we get
y = ex
y = e-x
From eqn (i) and (ii), we get
The perimeter of the curve r = 2 cos θ is:- a)1/2π
- b)π
- c)3/2π
- d)2π
Correct answer is option 'D'. Can you explain this answer?
The perimeter of the curve r = 2 cos θ is:
a)
1/2π
b)
π
c)
3/2π
d)
2π
|
|
Chirag Verma answered |
The curve is r = 2 cos θ
Changing it into Cartesian coordinate, we get
x2 + y2 = 2x
or, (x - l)2 + y2 = 1,
which is a circle with centre (1,0) and radius 1.
Hence
Perimeter = 2πr = 2π · 1 = 2π
Changing it into Cartesian coordinate, we get
x2 + y2 = 2x
or, (x - l)2 + y2 = 1,
which is a circle with centre (1,0) and radius 1.
Hence
Perimeter = 2πr = 2π · 1 = 2π
from x = 0 to x = 1, the x -axis and the ordinate at x = 1 is:
is equal to:
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