What is the integral of sin(2y) ?

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

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integral of sin(2y)

\int sin (2 y) d y

- \frac{1}{2} cos (2 y) + C

Solution steps

\int sin (2 y) d y

Apply u-substitution

: \int sin (u) \frac{1}{2} d u

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} (- cos (u))

Substitute back

u = 2 y

= \frac{1}{2} (- cos (2 y))

Simplify

= - \frac{1}{2} cos (2 y)

Add a constant to the solution

= - \frac{1}{2} cos (2 y) + C

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

y = 4^{\frac{x}{l n ( 2 )}}, at x = ln (16)

\int \frac{1}{5 x ^{2}} d x

\int_{0}^{l n (7)} x e^{x} d x

x \to 3 lim (\frac{x ^{3} - 1}{x - 1})