Suppose that f(x) is continuous, and that integral (-3,2) f(x) dx = 3, integral (-3,5) f(x) dx = -2, and integral (3,5) f(x) dx = 1. Then integral (2,3) f(x) dx = ?

Question

nathanjhw · Answer

-3
-6
3
5
6

nathanjhw · Answer

@dagrothus

anonymous · Answer

-6

nathanjhw · Answer

Alright thanks! Can you help me with another?

nathanjhw · Answer

Actually first, can you explain how you got that?

anonymous · Answer

the total integral from -3 to 5 is -2, you want to subtract off the integral from -3 to 2 and the integral from 3 to 5. 
-2 - 3 - 1 = -6

nathanjhw · Answer

I understand the -3, but why the minus 1 too?

nathanjhw · Answer

@dagrothus

anonymous · Answer

Think of the integral from 3 to 5 as part of the total integral. You want to remove that part because you only care about the integral from 2 to 3, so you subtract it from your total integral.

nathanjhw · Answer

Alright I think I understand. Can you help me with another similar one and I'll try the third on my own?

nathanjhw · Answer

Given that f(x) is continuous, integral (-2,2) f(x) dx = 7, integral (0,4) f(x) dx =-3, and integral (-2,4) f(x) dx = 2. Then integral (0,2) f(x) d(x) = ?

nathanjhw · Answer

2
4
-3
-6
0

nathanjhw · Answer

@dagrothus