Page 75 - Mathematics Class - XII

Case-Study Based Questions
Case-Study Based Questions

a
For any definite integral ∫ fx dx() .
0
1. Which of the following is correct
a a a a
(a) fx dx() fa xdx( ) (b) fx dx() f (2 x dx)

0 0 0 0
a a
(c) fx dx() fa xdx( ) (d) None of these
0 0
\2 \2
1
2
2. If I = logsin xdx and I = logcos xdx then
0 0
(a) I < I (b) I > I (c) I = I (d) None of these
1 2 1 2 1 2
\2
3. logsin xdx = ?
0
p
(a) log 2 (b) log (c) plog2 (d) 2 log 2
2
2 2
2 a
4. If f (2a – x) – f (x), then ∫ fx dx() = ?
0 a
∫
(a) 1 (b) 0 (c) 2 fx dx() (d) None of these
0
Assertion-Reason Based Questions
Assertion-Reason Based Questions

Directions for Questions 1 to 2: In each of the questions given below, there are two statements marked as
Assertion (A) and Reason (R). Mark your answer as per the codes provided below:
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false. (d) A is false but R is true.

b b
Q. 1. Assertion (A) : The value of ∫ ft dt() and ∫ fu du() are equal.
a a
Reason (R) : The value of definite integral of a function over any particular interval depends on
the function and the interval not on the variable of integration.

x
x
Q. 2. Assertion (A) : x sincos 2 xdx sincos 2 xdx
0 2 0
b ab b
Reason (R) : xf xdx() fx dx()
a 2 a
Answers

Case-Study Based Questions: 1. (a) 2. (c) 3. (b) 4. (b)

Assertion-Reason Based Questions: 1. (a) 2. (c)

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