What is the integral of sin(2t) ?

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

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integral of sin(2t)

\int sin (2 t) d t

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

Solution steps

\int sin (2 t) d t

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 t

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

Simplify

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

Add a constant to the solution

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

\int_{0}^{\frac{π}{4}} tan^{5} (x) d x

\int_{0}^{π} 19 sin^{2} (4 x) d x

\int t + 4 d t

f (x) = sin (sin (x)), at x = 3 π, 0

a^{x}