What is the integral of 2acos(θ/2) ?

The integral of 2acos(θ/2) is 4asin(θ/2)+C

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integral of 2acos(θ/2)

\int 2 a cos (\frac{θ}{2}) d θ

4 a sin (\frac{θ}{2}) + C

Solution steps

\int 2 a cos (\frac{θ}{2}) d θ

Take the constant out:

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

= 2 a \cdot \int cos (\frac{θ}{2}) d θ

Apply u-substitution

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

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

Use the common integral:

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

= 2 a \cdot 2 sin (u)

Substitute back

u = \frac{θ}{2}

= 2 a \cdot 2 sin (\frac{θ}{2})

Simplify

= 4 a sin (\frac{θ}{2})

Add a constant to the solution

= 4 a sin (\frac{θ}{2}) + C

\frac{d}{d x} (\frac{1}{2} x + 2)

(1 + cos^{2} (x))^{6}

t \to π lim (- 2 sin (- \frac{t}{2}))

\int_{0}^{\infty} a f (x) d x

x \to 2 + lim (ln ∣ x - 2 ∣)