Solve ∫ int(x^2+y^2)dsigma

$$\int \int ( x ^ { 2 } + y ^ { 2 } ) d \sigma$$

Evaluate

$$\sigma \left(xy^{2}+\frac{x^{3}}{3}\right)+С\sigma +С_{1}$$

Solution Steps

Find the integral of \int x^{2}+y^{2}\mathrm{d}x using the table of common integrals rule \int a\mathrm{d}\sigma =a\sigma .

$$\int x^{2}+y^{2}\mathrm{d}x\sigma$$

Simplify.

$$\left(\frac{x^{3}}{3}+y^{2}x+С\right)\sigma$$

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

$$\left(\frac{x^{3}}{3}+y^{2}x+С\right)\sigma +С$$

Differentiate w.r.t. x

$$\sigma \left(x^{2}+y^{2}\right)$$