# Thread: How do I find area between functions using integrals if...?

1. ## How do I find area between functions using integrals if...?

How do I find area between functions using integrals if there are more than two functions as shown in the attached pdf as #15?

Any input would be greatly appreciated!
2. Your points of intersection will be (1,1) and (2, 1/2). Split the area into two parts: the part of the area left and the part right of the line $x=1$ . On the left, your 'top' function will be y=x and your 'bottom' function will be y=x/4. On the right, y=1/x is the top and y=x/4 is the bottom. Therefore, your area will be
$A=\int_{0}^{1}\left(x-\frac{x}{4}\right)dx+\int_{1}^{2}\left(\frac{1}{x}-\frac{x}{4}\right)dx.$