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percibaa8

Answered question

2021-12-12

Use the methods introduced evaluate the following integrals.

\int \cos (\frac{x}{2} + \frac{π}{3}) d x

scomparve5j

Beginner2021-12-13Added 38 answers

Step 1
The integral is given as:

\int \cos (\frac{x}{2} + \frac{π}{3}) d x

Let

u = \frac{x}{2} + \frac{π}{3}

d u = \frac{1}{2} d x

Substitute the values in the given integral,

\int \cos (\frac{x}{2} + \frac{π}{3}) d x = \int 2 \cos u d u

2 \int \cos u d u = 2 \sin u + C

.
Step 2
Replace

u \Rightarrow (\frac{x}{2} + \frac{π}{3})

We get the integral solution is,

\int \cos (\frac{x}{2} + \frac{π}{3}) d x = 2 \sin (\frac{x}{2} + \frac{π}{3}) + C .

peterpan7117i

Beginner2021-12-14Added 39 answers

Given:

\int \cos (\frac{x}{2} + \frac{π}{3}) d x

Substitution

u = \frac{x}{2} + \frac{π}{3} \Rightarrow \frac{d u}{d x} = \frac{1}{2}

= 2 \int \cos (u) d u

Now we calculate:

\int \cos (u) d u

= \sin (u)

Substitute the already calculated integrals:

2 \int \cos (u) d u

= 2 \sin (u)

Reverse replacement

u = \frac{x}{2} + \frac{π}{3} :

= 2 \sin (\frac{x}{2} + \frac{π}{3})

Answer:

= 2 \sin (\frac{x}{2} + \frac{π}{3}) + C

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