What is the integral of sin(1/2)y ?

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

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integral of sin(1/2)y

\int sin (\frac{1}{2}) y d y

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

Solution steps

\int sin (\frac{1}{2}) y d y

Take the constant out:

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

= sin (\frac{1}{2}) \cdot \int y d y

Apply the Power Rule

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

= sin (\frac{1}{2}) \frac{y ^{2}}{2}

Simplify

sin (\frac{1}{2}) \frac{y ^{2}}{2} : \frac{1}{2} sin (\frac{1}{2}) y^{2}

= \frac{1}{2} sin (\frac{1}{2}) y^{2}

Add a constant to the solution

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

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

\int e^{t^{3}} t^{2} d t

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

\int 1.2 x d x

\int - \frac{1}{x 1 - x ^{2}} d x

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