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

Question 3

$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

Step 1: Start to Integrate

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Answer

To begin the integration process, we can recognize that the integral involves a constant multiplied by a cosine function. We will use the formula for integrating cosine, which states that ( \int \cos(kx) dx = \frac{1}{k} \sin(kx) + C ). In this case, we need to identify ( k ) as 4.

Step 2

Step 2: Complete Integration

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Answer

Thus, the integral can be computed as:

\int 7 \cos \left( 4x + \frac{\pi}{3} \right) dx = 7 \cdot \frac{1}{4} \sin \left( 4x + \frac{\pi}{3} \right) + C

This simplifies to:

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

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