Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Integral of Trigonometric Function
The integral presented is of the form:
\[
\int_{0}^{\pi} \sin \theta \cos^2 \theta \, d\theta
\]
where:
- The integration is carried out with respect to the variable \(\theta\).
- The limits of integration are from \(0\) to \(\pi\).
- \(\sin \theta\) and \(\cos \theta\) are trigonometric functions representing the sine and cosine of the angle \(\theta\), respectively.
- \(\cos^2 \theta\) means the square of \(\cos \theta\).
This integral involves integrating a function that is the product of \( \sin \theta \) and the square of \( \cos \theta \) over the interval from \(0\) to \(\pi\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F333de6cc-3da3-4bcc-9995-6ee1769198c2%2F5871d136-b085-4b52-aea3-bac430527305%2Fauhkfqv.jpeg&w=3840&q=75)
Transcribed Image Text:### Integral of Trigonometric Function
The integral presented is of the form:
\[
\int_{0}^{\pi} \sin \theta \cos^2 \theta \, d\theta
\]
where:
- The integration is carried out with respect to the variable \(\theta\).
- The limits of integration are from \(0\) to \(\pi\).
- \(\sin \theta\) and \(\cos \theta\) are trigonometric functions representing the sine and cosine of the angle \(\theta\), respectively.
- \(\cos^2 \theta\) means the square of \(\cos \theta\).
This integral involves integrating a function that is the product of \( \sin \theta \) and the square of \( \cos \theta \) over the interval from \(0\) to \(\pi\).
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