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

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

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integral of sin(1/2 x)

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

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

Solution steps

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

Apply u-substitution

= \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 \int sin (u) d u

Use the common integral:

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

= 2 (- cos (u))

Substitute back

u = \frac{1}{2} x

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

Simplify

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

Add a constant to the solution

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

3 y^{^{''}} + 11 y^{^{'}} + 6 y = 3 x^{2} + 7 x + 3

\frac{d P}{d t} = k P^{1.01}, P (0) = 10

\frac{d ^{2}}{d x ^{2}} (cos (5 x))

x \to 0 lim (\frac{a ^{x} - b ^{x}}{x})

n or ma l y = 2 x^{2}, (- 2, 8)

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