What is the integral of sin(x)y ?

The integral of sin(x)y is -ycos(x)+C

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integral of sin(x)y

\int sin (x) y d x

- y cos (x) + C

Solution steps

\int sin (x) y d x

Take the constant out:

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

= y \cdot \int sin (x) d x

Use the common integral:

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

= y (- cos (x))

Simplify

= - y cos (x)

Add a constant to the solution

= - y cos (x) + C

f (t) = t^{3}

\int_{- 1}^{1} e^{2 x - 2} d x

\int cot (t) d t

x \to - 2 lim (\frac{1}{x + 2})

\int sec^{2} (1 - 4 x) d x