Solve ∫ 4-4x^2

$$\int 4 - 4 x ^ { 2 }$$

Evaluate

$$-\frac{4x^{3}}{3}+4x+С$$

Solution Steps

Integrate the sum term by term.

$$\int 4\mathrm{d}x+\int -4x^{2}\mathrm{d}x$$

Factor out the constant in each of the terms.

$$\int 4\mathrm{d}x-4\int x^{2}\mathrm{d}x$$

Find the integral of 4 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$4x-4\int x^{2}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{2}\mathrm{d}x with \frac{x^{3}}{3}. Multiply -4 times \frac{x^{3}}{3}.

$$4x-\frac{4x^{3}}{3}$$

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

$$4x-\frac{4x^{3}}{3}+С$$

Differentiate w.r.t. x

$$4-4x^{2}$$