- #1

- 132

- 1

## Main Question or Discussion Point

I know the title can be a bit misleading, yet it's really close to what I want to ask.

Today I came upon an integral at school. The really easy one :[itex]\int_{-1}^{1}x^3 dx[/itex]. Of course, calculating the integral, you get 0. Yet, as far as I know, the way to get the area under the curve is by integrating the function inside the limits of which the area above or under x you want to get.

Yet [itex]f(x)=x^3[/itex] occupies some space from -1 to 0, and the same space from 0 to 1. Why then does the integral consider the one being positive space and the other one being negative, sum them up and calculate the area as zero? This is a question that I've had before, and by looking I saw that there are restrictions or,lack of a better word, modifications that must be applied to the integral when calculating for the area under the curve. Could you please introduce me to them?

Thanks in advance!

Today I came upon an integral at school. The really easy one :[itex]\int_{-1}^{1}x^3 dx[/itex]. Of course, calculating the integral, you get 0. Yet, as far as I know, the way to get the area under the curve is by integrating the function inside the limits of which the area above or under x you want to get.

Yet [itex]f(x)=x^3[/itex] occupies some space from -1 to 0, and the same space from 0 to 1. Why then does the integral consider the one being positive space and the other one being negative, sum them up and calculate the area as zero? This is a question that I've had before, and by looking I saw that there are restrictions or,lack of a better word, modifications that must be applied to the integral when calculating for the area under the curve. Could you please introduce me to them?

Thanks in advance!