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Popular >

integral of-1/2 y

Solution

\int - \frac{1}{2} y d y

Solution

- \frac{y ^{2}}{4} + C

Solution steps

\int - \frac{1}{2} y 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 d y

Apply the Power Rule

: \frac{y ^{2}}{2}

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

Simplify

- \frac{1}{2} \cdot \frac{y ^{2}}{2} : - \frac{y ^{2}}{4}

= - \frac{y ^{2}}{4}

Add a constant to the solution

= - \frac{y ^{2}}{4} + C

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\frac{d y}{d x} = \frac{( x ^{2} y - y )}{( y + 1 )}, y (0) = 1

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Frequently Asked Questions (FAQ)

What is the integral of-1/2 y ?
The integral of-1/2 y is -(y^2)/4+C