Integration by Geometry

Convert the function into several geometric separate functions that are easily evalutable like:

• Semicircle $y=\sqrt{1-x^2}$
• Triangle $y=x-5$ and then, you can easily compute the integral by summing each integral of each component

Example

${\int }_0^{1}f(x)dx$ $f(x)=\sqrt{1-x^2}$ $⟹y^2=1-x^2$ $⟹y^2+x^2=1$ We know how to graph this. This is a circle with a radius of 1 and centered at (0,0).