Topic: Chapter 11: Integral Calculus



Topic: Chapter 11: Integral Calculus
Q.1
If ∫ f (x)dx = g(x) + c, then ∫ f (x)g′(x)dx 
A. ∫(f (x))2 dx
B. f (x)g(x)dx
C. f ′(x)g(x)dx
D. ∫(g(x))2 dx
Answer : Option A
Explaination / Solution:
No Explaination.


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Q.2
If , then the value of k is
A. log 3
B. − log 3
C. – 1 / log 3
D. 1 / log 3
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.3
If  ∫ f ′(x)ex2dx = (x − 1)ex2 + c , then f(x) is
A. 2x3x2/2 + x + c 
B. x3/2 + 3x2 + 4x + c 
C. x3 + 4x2 + 6x + c 
D. 2x3/3 - x2+ x+ c
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.4
The gradient (slope) of a curve at any point (x, y) is [x2 – 4]/ x2 . If the curve passes through the point (2, 7), then the equation of the curve is
A. y = x + 4/x + 3
B. y = x + 4/x + 4 
C. y = x2 + 3x + 4
D. y = x2 − 3x + 6
Answer : Option A
Explaination / Solution:
No Explaination.


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Q.5
 is
A. cot(xex ) + c
B. sec(xex ) + c
C. tan(xex ) + c
D. cos( xex ) + c
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.6
 is 
A. tan x + c
B. 2tan x + c
C. ½ tan x + c
D. ¼ tan x + c
Answer : Option A
Explaination / Solution:
No Explaination.


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Q.7
∫sin3xdx is
A.
B.
C.
D.
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.8
 is
A. x + c
B. [ x3/3] + c
C. [3/ x3] + c
D. [1/ x2] + c
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.9

A. tan−1 (sin x ) + c
B. 2sin−1 (tan x ) + c
C. tan−1 (cos x ) + c
D. sin−1 (tan x ) + c
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.10
  is
A. x2 + c
B. 2x2 + c
C. x2/2 + c
D. − x2/2  + c
Answer : Option C
Explaination / Solution:
No Explaination.


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