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

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

Popular >

integral of 2cos(1/2 x)

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

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

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= 2 \cdot 2 sin (u)

Substitute back

u = \frac{1}{2} x

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

Simplify

= 4 sin (\frac{1}{2} x)

Add a constant to the solution

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

\frac{\partial}{\partial y} (4 x^{3} y^{2} - 2 x y^{3})

x^{3} + 7 e^{x}

\frac{x d y}{d x} = y^{2} - 4

\frac{d y}{d x} = (\frac{y}{x} + \frac{1}{4})^{2}

y = (f (x))^{2}, at x = 0

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