Question

Given that ∫ 0 1 f ( x ) d x = 1 , ∫ 6 3 f ( x ) d x = 6 and ∫ 7 1 f ( x ) d x = 7 . Find ∫ 7 6 f ( x ) d x .

Answer 1

Step-by-step explanation:

Correct option is

C

5

∫

−1

4

f(x)dx=4 and ∫

2

4

[3−f(x)dx=7]

F(4)−F(−1)=4 →(1)

and 3∣x∣

2

4

−[F(4)−F(2)]=7

[F(4)−F(2)]=6−7=−1

∴ F(4)−F(2)=−1→(2)

∫

−1

2

f(x)dx=F(2)−F(−1)→(3)

eqn.(1)-eqn.(2), we get F(2)−F(−1)=5

∴ ∫

−1

2

f(x)dx=

5

(put value in eqn.(3) )