Integral Calculus Mcqs​

Integral Calculus Mcqs

Question 1.
10(ex + e-x) dx is:
(a) e – e-1
(b) e-1 – e
(c) e + e1
(d) None
Solution :
(a) is correctQuestion 2.

8x2(x3+2)3dx is equal to: [1 Mark, Nov. 2006]
(a) –43(x3 + 2) + C
(b) –43(x3 + 2)-2 + C
(c) 43(x3 + 2)2 + C
(d) None of these
Answer B] Is Correct

Question 3.

dxx2+a2:
(a) 12log(x + x2+a2−−−−−−√) + C
(b) log(x + x2+a2−−−−−−√) + C
(c) log(xx2+a2−−−−−−√) + C
(d) 12log(xx2+a2−−−−−−√) + C
Answer:
(b) is correct
I. Remember it as Formula
Trick II. Go by choices
Differentiation of which option is the Integration of given Function
Here to differentiate is more easy than to Integrate.
Integral Calculus – CA Foundation Maths Study Material 3

Question 4.
The value of 20xx+2xdx is: [1 Mark, Feb. 2007 & May 2007]
(a) 0
(b) 3
(c) 2
(d) 1
Answer:
(d) is correct
Question 5.

The Integral of (e3x + e-3x)/ex is: [1 Mark, May 2007]
(a) e2x2+e4x4 + C
(b) e2x2e4x4 + C
(c) e2x – e-4x
(d) None of these
Answer:
(b) is correct
Integral Calculus – CA Foundation Maths Study Material 6
Where c = Integration (Arbitrary) Constant.

Question 6.

∫x2e3xdx is:
(a) x2.e3x – 2xe3x + 2e3x + C
(b) e3x3xe3x9 + 2e3x + C
(c) x2e3x32xe3x9+227e3x + C
(d) None of these
Answer:
(c) is correct.

Question 7.
212x1+x2dx: [1 Mark, May & Aug. 2007]
(a) loge52
(b) loge5 – loge2 + 1
(a) loge25
(d) None of these
Answer:
(a) is correct

Question 8.
The value of e1(1+logx)xdx is: [Given Loge = 1]. [1 Mark, Aug. 2007]
(a) 1/2
(b) 3/2
(c) 1
(d) 5/2
Answer:
(b) is correct

Question 9.
Find ∫x3(x2+1)3dx: [1 Mark, Aug. 2007]
Integral Calculus – CA Foundation Maths Study Material 10
Answer:
(b) is correct

Question 10.
1x2a2dx is: [1 Mark, Nov. 2007]
(a) log(x – a) – log(x + a) + C
(b) log x – ax+a + C
(c) 12a log(xax+a) + C
(d) None of these
Answer:
(c) is correct

Question 11.

The value of 10dx(1+x)(2+x) is : 
(a) log 34
(b) log 43
(c) log 12
(d) None of these
Answer:
(b) is correct
10dx(1+x)(2+x)
By Hit & Trial Method; we get
10(11+x12+x)dx
= [log(1 + x)]10 – [log(2 + x)]10
= [log(1 + 1)- log(1 + 0)] – [log(2 + 1) – log(2 + 0)]
= log2 – 0 – log3 + log2
= 2log2 – log3
= log22 – log3 = log43

Question 12.

The value of 32(5 – x)dx – 32f(x)dx is:
Answer:
(b) is correct.

Question 13.
elogexxdxx is:
(a) x-1 + C
(b) x + c
(c) x2 + C
(d) None
Answer:
(b) is correct
elogexdxx = ∫xx
[Formula ax logab = bx]
= ∫dx = x + c

Question 14.
Evaluate ∫1(x1)(x2)dx: [1 Mark, June 2008]
(a) log (x2x1) + C
(b) log[(x – 2)(x -1)] + C
(c) (x1x2) + C
(d) None
Answer:
(a) is correct,
1(x1)(x2) = ∫(1(x2)1x1)
(By Hit & Trial method)
= log(x – 2)- log(x -1)+ c
= log(x2x1) + c

Question 15.
41(2x + 5) dx and the value is: [1 Mark, June 2008]
(a) 10
(b) 3
(c) 30
(d) None
Answer:
(c) Is correct.
Integral Calculus – CA Foundation Maths Study Material 14
= 15 + 15 = 30

Question 16.

1x(x51)dx
Integral Calculus – CA Foundation Maths Study Material 15
Answer:
(b) is correct

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