What is the integral of 7sin(θ/3) ?

The integral of 7sin(θ/3) is -21cos(θ/3)+C

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integral of 7sin(θ/3)

\int 7 sin (\frac{θ}{3}) d θ

- 21 cos (\frac{θ}{3}) + C

Solution steps

\int 7 sin (\frac{θ}{3}) d θ

Take the constant out:

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

= 7 \cdot \int sin (\frac{θ}{3}) d θ

Apply u-substitution

: \int sin (u) \cdot 3 d u

= 7 \cdot \int sin (u) \cdot 3 d u

Take the constant out:

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

= 7 \cdot 3 \cdot \int sin (u) d u

Use the common integral:

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

= 7 \cdot 3 (- cos (u))

Substitute back

u = \frac{θ}{3}

= 7 \cdot 3 (- cos (\frac{θ}{3}))

Simplify

= - 21 cos (\frac{θ}{3})

Add a constant to the solution

= - 21 cos (\frac{θ}{3}) + C

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