What is the integral of-sin(-x+2) ?

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

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integral of-sin(-x+2)

\int - sin (- x + 2) d x

- cos (- x + 2) + C

Solution steps

\int - sin (- x + 2) d x

Take the constant out:

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

= - \int sin (- x + 2) d x

Apply u-substitution

: \int - sin (u) d u

= - \int - sin (u) d u

Take the constant out:

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

= - (- \int sin (u) d u)

Use the common integral:

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

= - (- (- cos (u)))

Substitute back

u = - x + 2

= - (- (- cos (- x + 2)))

Simplify

= - cos (- x + 2)

Add a constant to the solution

= - cos (- x + 2) + C

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