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

The integral of 2sin(t/2) is -4cos(t/2)+C

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integral of 2sin(t/2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int sin (u) \cdot 2 d u

= 2 \cdot \int sin (u) \cdot 2 d u

Take the constant out:

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

= 2 \cdot 2 \cdot \int sin (u) d u

Use the common integral:

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

= 2 \cdot 2 (- cos (u))

Substitute back

u = \frac{t}{2}

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

Simplify

= - 4 cos (\frac{t}{2})

Add a constant to the solution

= - 4 cos (\frac{t}{2}) + C

4 cos (x)

\frac{\partial}{\partial x} (y - 2 ln ∣ y ∣ + x y)

\int x \cdot e^{- 2 x^{2}} d x

\frac{d}{d x} (a x + b)

\frac{d}{d x} (\frac{2 x ^{2}}{4 - x ^{2}})