Solve ∫ (-4y) wrt y

$$\int ( - 4 y ) d y$$

Evaluate

$$С-2y^{2}$$

Solution Steps

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

$$-4\int y\mathrm{d}y$$

Since \int y^{k}\mathrm{d}y=\frac{y^{k+1}}{k+1} for k\neq -1, replace \int y\mathrm{d}y with \frac{y^{2}}{2}. Multiply -4 times \frac{y^{2}}{2}.

$$-2y^{2}$$

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

$$-2y^{2}+С$$

Differentiate w.r.t. y

$$-4y$$