What is the integral of sin(3θ) ?

The integral of sin(3θ) is -1/3 cos(3θ)+C

Popular >

integral of sin(3θ)

\int sin (3 θ) d θ

- \frac{1}{3} cos (3 θ) + C

Solution steps

\int sin (3 θ) d θ

Apply u-substitution

: \int sin (u) \frac{1}{3} d u

= \int sin (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{1}{3} (- cos (u))

Substitute back

u = 3 θ

= \frac{1}{3} (- cos (3 θ))

Simplify

= - \frac{1}{3} cos (3 θ)

Add a constant to the solution

= - \frac{1}{3} cos (3 θ) + C

f (x) = e^{2 x}, at x = \frac{1}{2} ln (3)

(\frac{t ^{3}}{t ^{6} + 7})^{2}

\int \frac{x}{16 + x ^{2}} d x

x \to 3 lim (2 x + ∣ x - 3 ∣)

x \to 7 lim (\frac{x + 5}{x + 9})