Integral Question

Question

Suppose that ∫³_-1f(x)dx = 4 and ∫³₅f(x)dx = 1. Find ∫^-1₅ (2f(x) - 3)dx

a. -10

b. 0

c. 3

d. 6

e. 10

f. 12

Answer 1

∫³_-1f(x)dx = 4 and ∫⁵₃f(x)dx=- ∫³₅f(x)dx = -1; So ∫⁵_-1f(x)dx=3.

Also ∫^-1₅ (2f(x) - 3)dx=-2∫^-5_-1 f(x) dx+∫5_-1 3dx=-2*3+18=12;

Answer is f.

Answer 2

I'm getting the ∫_-1⁵f(x)dx = 5 becuase it's 4+1, so the integral from 5 to -1 = -5... now it wants 2*f(x) so integrate and get -10 then subtract ∫₅^-1 3dx = -18 so 10 - -18 = 8 but that's not an answer for some reason