Find the value of the definite integral if you know that...

Question

13.5 8.5 13.5 11

∫ f(x)dx = 2 ∫ f(x)dx = 8 ∫ f(x)dx = 8 ∫ f(x)dx = -14

6 6 11 8.5

Find the value of...

8.5

∫ (2f(x)-8)dx = ?

11

Answer 1

∫₁₁^8.5 (2f(x)-8)dx = 2∫₁₁^8.5 f(x)dx - 8∫₁₁^8.5dx = -2∫¹¹_8.5 f(x)dx - 8∫₁₁^8.5dx

=-2(-14) -8(8.5-11)

= 28+20 = 48