Solve int int ∫ (from 4 pi to 4) of d u wrt ydz

$$\int \int \int _ { 4 \pi } ^ { 4 } d u d y d z$$

Evaluate

$$Сz+4\left(1-\pi \right)yz+С_{1}$$

Solution Steps

Find the integral of \int \int _{4\pi }^{4}1\mathrm{d}u\mathrm{d}y using the table of common integrals rule \int a\mathrm{d}z=az.

$$\int \int _{4\pi }^{4}1\mathrm{d}u\mathrm{d}yz$$

Simplify.

$$\left(\left(-4\pi +4\right)y+С\right)z$$

If F\left(z\right) is an antiderivative of f\left(z\right), then the set of all antiderivatives of f\left(z\right) is given by F\left(z\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\left(\left(-4\pi +4\right)y+С\right)z+С$$

Differentiate w.r.t. y

$$4z-4\pi z$$