What is the integral of 2sin(θ)cos(θ) ?

The integral of 2sin(θ)cos(θ) is sin^2(θ)+C

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integral of 2sin(θ)cos(θ)

\int 2 sin (θ) cos (θ) d θ

sin^{2} (θ) + C

Solution steps

\int 2 sin (θ) cos (θ) d θ

Take the constant out:

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

= 2 \cdot \int sin (θ) cos (θ) d θ

Apply u-substitution

: \int u d u

= 2 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 2 \cdot \frac{u ^{2}}{2}

Substitute back

u = sin (θ)

= 2 \cdot \frac{sin ^{2} ( θ )}{2}

Simplify

2 \cdot \frac{sin ^{2} ( θ )}{2} : sin^{2} (θ)

= sin^{2} (θ)

Add a constant to the solution

= sin^{2} (θ) + C

\frac{d}{d x} (\frac{x + 3}{x})

f (x) = x^{3} - 2 x^{2}

x \to \infty lim (- 5 x)

x^{4} + y^{3} x^{5} + 4 y^{^{'}} = 0, y (0) = 0

\frac{\partial}{\partial x} (\frac{x y}{x ^{2} + y ^{2}})

What is the integral of 2sin(θ)cos(θ) ?
The integral of 2sin(θ)cos(θ) is sin^2(θ)+C