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- TL;DR Summary
- I am interested whether we can get a negative area above the x-axis when the lower limit of integration is larger than the upper limit of integration

Suppose the following integration,

##\int_3^{-1} x^2 \, dx = \frac{1}{3}(-1)^3 - \frac{1}{3}(3)^3 = -\frac{28}{3}##

However, if we have a look at the graph,

The area between ##x = 3## and ##x = -1## is above the x-axis so should be positive. Dose anybody please know why the I am getting negative area from the integral?

Many thanks!

##\int_3^{-1} x^2 \, dx = \frac{1}{3}(-1)^3 - \frac{1}{3}(3)^3 = -\frac{28}{3}##

However, if we have a look at the graph,

The area between ##x = 3## and ##x = -1## is above the x-axis so should be positive. Dose anybody please know why the I am getting negative area from the integral?

Many thanks!