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Popular >

integral of-(y^2)/2

Solution

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

Solution

- \frac{y ^{3}}{6} + C

Solution steps

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

Take the constant out:

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

= - \frac{1}{2} \cdot \int y^{2} d y

Apply the Power Rule

: \frac{y ^{3}}{3}

= - \frac{1}{2} \cdot \frac{y ^{3}}{3}

Simplify

- \frac{1}{2} \cdot \frac{y ^{3}}{3} : - \frac{y ^{3}}{6}

= - \frac{y ^{3}}{6}

Add a constant to the solution

= - \frac{y ^{3}}{6} + C

Popular Examples

derivative of (2x^2)/(6x+5)derivative of

\frac{2 x ^{2}}{6 x + 5}

integral from 0 to ln(2) of e^{3x}

\int_{0}^{l n (2)} e^{3 x} d x

derivative of x/(sqrt(y))

\frac{d}{d x} (\frac{x}{y})

integral of 4/(sqrt(x)(x+6))

\int \frac{4}{x ( x + 6 )} d x

y^'=(x^2+y^2)/(xy),y(1)=1

y^{^{'}} = \frac{x ^{2} + y ^{2}}{x y}, y (1) = 1

Frequently Asked Questions (FAQ)

What is the integral of-(y^2)/2 ?
The integral of-(y^2)/2 is -(y^3)/6+C