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Popular >

integral of y(1-y)

Solution

\int y (1 - y) d y

Solution

\frac{y ^{2}}{2} - \frac{y ^{3}}{3} + C

Solution steps

\int y (1 - y) d y

Expand

y (1 - y) : y - y^{2}

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

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

\int y^{2} d y = \frac{y ^{3}}{3}

= \frac{y ^{2}}{2} - \frac{y ^{3}}{3}

Add a constant to the solution

= \frac{y ^{2}}{2} - \frac{y ^{3}}{3} + C

Popular Examples

integral of 1/((x^2-2)(x^2+2))

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

integral of y/(ln(y))

\int \frac{y}{ln ( y )} d y

integral of e^x3x

\int e^{x} 3 x d x

integral of x^3sqrt(49+x^2)

\int x^{3} 49 + x^{2} d x

integral of x^2+x-12

\int x^{2} + x - 12 d x

Frequently Asked Questions (FAQ)

What is the integral of y(1-y) ?
The integral of y(1-y) is (y^2)/2-(y^3)/3+C