Solve ∫ -z^2 wrt z

$$\int - z ^ { 2 } d z$$

Evaluate

$$-\frac{z^{3}}{3}+С$$

Solution Steps

Factor out the constant using \int af\left(z\right)\mathrm{d}z=a\int f\left(z\right)\mathrm{d}z.

$$-\int z^{2}\mathrm{d}z$$

Since \int z^{k}\mathrm{d}z=\frac{z^{k+1}}{k+1} for k\neq -1, replace \int z^{2}\mathrm{d}z with \frac{z^{3}}{3}.

$$-\frac{z^{3}}{3}$$

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.

$$-\frac{z^{3}}{3}+С$$

Differentiate w.r.t. z

$$-z^{2}$$