What is the integral of y(1-x^2) ?

The integral of y(1-x^2) is (y^2(1-x^2))/2+C

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integral of y(1-x^2)

\int y (1 - x^{2}) d y

\frac{y ^{2} ( 1 - x ^{2} )}{2} + C

Solution steps

\int y (1 - x^{2}) d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (1 - x^{2}) \cdot \int y d y

\int y d y = \frac{y ^{2}}{2}

= (1 - x^{2}) \frac{y ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ^{2} ( 1 - x ^{2} )}{2}

Add a constant to the solution

= \frac{y ^{2} ( 1 - x ^{2} )}{2} + C