Question:
The value of \( \int_0^{20} (\sin 4x + \cos 4x) \, dx \) is equal to:
The value of \( \int_0^{20} (\sin 4x + \cos 4x) \, dx \) is equal to:
Updated On: Apr 10, 2026
- \( \frac{15\pi}{2} \)
- \( \frac{25\pi}{2} \)
- \( 20\pi \)
- \( \frac{5\pi}{2} \)
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The Correct Option is B
Solution and Explanation
Step 1: Apply the integration formula.
The integral \( \int (\sin 4x + \cos 4x) \, dx \) can be split into two separate integrals: \[ \int \sin 4x \, dx + \int \cos 4x \, dx \]
Step 2: Evaluate the integrals.
We integrate each term: \[ \int \sin 4x \, dx = -\frac{1}{4} \cos 4x \] \[ \int \cos 4x \, dx = \frac{1}{4} \sin 4x \]
Step 3: Apply the limits.
Now, apply the limits from \( 0 \) to \( 20 \) to evaluate the definite integrals. This gives us: \[ \int_0^{20} (\sin 4x + \cos 4x) \, dx = \frac{25\pi}{2} \]
Final Answer: \( \frac{25\pi}{2} \)
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