What is the integral of sin((2t)/7) ?

The integral of sin((2t)/7) is -7/2 cos((2t)/7)+C

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integral of sin((2t)/7)

\int sin (\frac{2 t}{7}) d t

- \frac{7}{2} cos (\frac{2 t}{7}) + C

Solution steps

\int sin (\frac{2 t}{7}) d t

Apply u-substitution

: \int sin (u) \frac{7}{2} d u

= \int sin (u) \frac{7}{2} d u

Take the constant out:

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

= \frac{7}{2} \cdot \int sin (u) d u

Use the common integral:

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

= \frac{7}{2} (- cos (u))

Substitute back

u = \frac{2 t}{7}

= \frac{7}{2} (- cos (\frac{2 t}{7}))

Simplify

= - \frac{7}{2} cos (\frac{2 t}{7})

Add a constant to the solution

= - \frac{7}{2} cos (\frac{2 t}{7}) + C

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What is the integral of sin((2t)/7) ?
The integral of sin((2t)/7) is -7/2 cos((2t)/7)+C