Question

Find the integral:

∫−20(x+5)dx

Answer 1

`-20\left((x^2)/(2)+5x\right)+C`

Explanation:

`\int \:-20\left(x+5\right)dx`

`\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx`

`-20\cdot \int \:x+5dx`

`\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx`

`-20\left(\int \:xdx+\int \:5dx\right)`

`=-20\left((x^2)/(2)+5x\right)`

`\mathrm{Add\:a\:constant\:to\:the\:solution}`

`=-20\left((x^2)/(2)+5x\right)+C`