What is the integral of-sin(x)*cos(x) ?

The integral of-sin(x)*cos(x) is -(sin^2(x))/2+C

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integral of-sin(x)*cos(x)

\int - sin (x) \cdot cos (x) d x

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

Solution steps

\int - sin (x) cos (x) d x

Take the constant out:

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

= - \int sin (x) cos (x) d x

Apply u-substitution

= - \int u d u

Apply the Power Rule

= - \frac{u ^{2}}{2}

Substitute back

u = sin (x)

= - \frac{sin ^{2} ( x )}{2}

Add a constant to the solution

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

What is the integral of-sin(x)*cos(x) ?
The integral of-sin(x)*cos(x) is -(sin^2(x))/2+C