# Intuition for negative integrals

Author:
scnc1111

## Directions

Intuition 1: 1. Notice that the area under the curve from 0 to π is 2. 2. Drag b (slider or point) to 2π. Notice that the integral is 0. 3. Drag a (slider or point) to π. Notice that the integral is -2. ⇒ this brings out the fact that if the curve is under the x axis, then the integral is negative. If you want to find the area between the curve sin(x) and the x-axis from 0 to 2π, you have to be ware that first find the area between 0 and π (= 2), and then add this to the magnitude of the area from π to 2π (= |-2|). i.e. Intuition 2: 1. Now try dragging b (slider or point) to 0 (and a remains in π). Notice that the integral is -2. 2. Invert a and b. Notice that the integral becomes 2. 3. Drag ﻿b to -π and ﻿a to 0. Notice that now the integral is 2. 4. Invert a and b. Notice that the integral becomes -2. ⇒ this brings out the fact that if you invert the limits ﻿a and ﻿﻿bi﻿﻿﻿n an integral, the sign of the integral gets inverted. i.e.