43. ∫0^π / 2cos 5 t cos 10 t d t

Name: 43. ∫0^π / 2cos 5 t cos 10 t d t
Uploaded: 2021-03-16T19:28:08-08:00
Duration: 3 min 40 s
Channel: Nafis Fuad
Description: 43. ∫0^π / 2cos 5 t cos 10 t d t

First, we can use the product-to-sum identity for cosine, which states that ( cos a cos b =

Question

43. \( \int_{0}^{\pi / 2} \cos 5 t \cos 10 t d t \)

          43. \( \int_{0}^{\pi / 2} \cos 5 t \cos 10 t d t \)

Added by Catherine E.

Calculus

James Stewart 8th Edition

Chapter 7

Instant Answer

Solved by Expert Nafis Fuad

03/16/2021

Step 1

Applying this to our integral, we get: \( \int_{0}^{\pi / 2} \cos 5 t \cos 10 t d t = \frac{1}{2} \int_{0}^{\pi / 2} [\cos(5t - 10t) + \cos(5t + 10t)] dt \) Simplifying the terms inside the integral, we get: \( = \frac{1}{2} \int_{0}^{\pi / 2} [\cos(-5t) + Show more…

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