# 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
Intuition 2:
1. Now try dragging

**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.**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 **b**in an integral, the sign of the integral gets inverted. i.e.