What is the integral from x to 2-x of (x^2+y^2) ?

The integral from x to 2-x of (x^2+y^2) is 2x^2-2x^3+(8-12x+6x^2-2x^3)/3

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integral from x to 2-x of (x^2+y^2)

\int_{x}^{2 - x} (x^{2} + y^{2}) d y

2 x^{2} - 2 x^{3} + \frac{8 - 12 x + 6 x ^{2} - 2 x ^{3}}{3}

Solution steps

\int_{x}^{2 - x} x^{2} + y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{x}^{2 - x} x^{2} d y + \int_{x}^{2 - x} y^{2} d y

\int_{x}^{2 - x} x^{2} d y = 2 x^{2} - 2 x^{3}

\int_{x}^{2 - x} y^{2} d y = \frac{8 - 12 x + 6 x ^{2} - 2 x ^{3}}{3}

= 2 x^{2} - 2 x^{3} + \frac{8 - 12 x + 6 x ^{2} - 2 x ^{3}}{3}

\int_{1}^{2} x^{3} \cdot ln (x) d x

\int_{0}^{a} 2 x - x^{2} d x

\int_{1}^{2} \frac{2 ^{x}}{x} d x

\int_{- 2 x}^{x} \frac{1}{csc ^{5} ( t )} d t

\int_{0}^{2} 5 x^{2} - 8 x + 4 d x

What is the integral from x to 2-x of (x^2+y^2) ?
The integral from x to 2-x of (x^2+y^2) is 2x^2-2x^3+(8-12x+6x^2-2x^3)/3