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Find $$\int 7 \cos\left( 4x + \frac{\pi}{3} \right) dx.$$ - Scottish Highers Maths - Question 3 - 2023

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$Find--$$\int-7-\cos\left(-4x-+-\frac{\pi}{3}-\right)-dx.$$-Scottish Highers Maths-Question 3-2023.png$

Find $$\int 7 \cos\left( 4x + \frac{\pi}{3} \right) dx.$$

Worked Solution & Example Answer:Find $$\int 7 \cos\left( 4x + \frac{\pi}{3} \right) dx.$$ - Scottish Highers Maths - Question 3 - 2023

Step 1

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Answer

To begin the integration of the function, we can factor out the constant multiplier from the integral:

$\int 7 \cos\left( 4x + \frac{\pi}{3} \right) dx = 7 \int \cos\left( 4x + \frac{\pi}{3} \right) dx.$

Step 2

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Answer

Next, we need to find the integral of the cosine function. The result of the integral is given by:

$7 \cdot \frac{1}{4} \sin\left( 4x + \frac{\pi}{3} \right) + C,$ where $C$ is the constant of integration.

Thus, the final answer is:

$\frac{7}{4} \sin\left( 4x + \frac{\pi}{3} \right) + C.$

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