What is the integral of 2sin(1/2 x) ?

The integral of 2sin(1/2 x) is -4cos(1/2 x)+C

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integral of 2sin(1/2 x)

\int 2 sin (\frac{1}{2} x) d x

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

Solution steps

\int 2 sin (\frac{1}{2} x) d x

Take the constant out:

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

= 2 \cdot \int sin (\frac{1}{2} x) d x

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{1}{2} x

= 2 \cdot 2 (- cos (\frac{1}{2} x))

Simplify

= - 4 cos (\frac{1}{2} x)

Add a constant to the solution

= - 4 cos (\frac{1}{2} x) + C

\frac{d}{d x} (300 x - 10 x^{2} + \frac{x ^{3}}{3})

\int_{0}^{1} 8 e^{- 2 x} d x

x \to 8 lim (x - 8)

\frac{10 s - 3}{s ^{2} + 4 s + 29}

f (x) = sin (x), at x = \frac{5 π}{2}

What is the integral of 2sin(1/2 x) ?
The integral of 2sin(1/2 x) is -4cos(1/2 x)+C