What is ∫-7^-1 f(x)dx?
suppose that f(x) is an even function and let ∫0^1 f(x)dx = 5 and ∫0^7 f(x)dx = 1. What is ∫-7^-1 f(x)dx?
This is my work
I expand ∫-7^-1 f(x)dx to F(-1) - F(-7)
F(-1) - F(-7) is the same thing as F(1) - F(7) since it is an even function
plug in the values to get 5-1, which equals 4
I strongly believe that the answer is 4, however, on the test my teacher is saying it's -4. I talked to her about it and she did not listen. Could someone show me if I am right, or if the answer is indeed -4?
Also, I wasn't really sure how to write the definite integral on the keyboard, so if you didn't get what I mean by ∫-7^-1, I meant to say that the lower limit is -7 and the upper limit is -1