6.1-7.1 Formulas

Average value of a function

favg=\frac{1}{b-a}\int_{a}^{b}f\left(x\right)\differentialD x

Area between curves

A=\int_{a}^{b}\left(upperfunction\right)-\left(lowerfunction\right)\differentialD x

A=\int_{a}^{b}\left(rightfunction\right)-\left(leftfunction\right)\differentialD y

Disk method

V=\int_{a}^{b}A\left(x\right)\differentialD x

V=\int_{a}^{b}A\left(y\right)\differentialD y

Area of a solid disk

$$A=\pi\left(radius\right)^2$$

Area of a ring

A=\pi\left(\left(outerradius\right)\right)^2-\left(\imaginaryI nnerradius\right)^2)

Method of Cylinders

$$A=2\pi rh$$

Integration by parts

$$\int_{}^{}u\cdot dv=u\cdot v\int_{}^{}v\cdot du$$

$$\int_{a}^{b}u\cdot dv=u\cdot v\left|b-a\right|-\int_{a}^{b}v\cdot du$$