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Find of region area 7₁ f(x) = 6 sin x + g(x) = 6 los 2x - 1/2 ≤ x ≤ To Keep 4 demials. L XL

Find of region area 7₁ f(x) = 6 sin x + g(x) = 6 los 2x - 1/2 ≤ x ≤ To Keep 4 demials. L XL

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Certainly! Below is the transcription and explanation suited for an educational website: --- **Mathematics Problems** **1. Area of the Region** Find the area of the region between the functions: - \( f(x) = 6 \sin x \) - \( g(x) = 6 \cos 2x \) over the interval \( -\frac{\pi}{2} \leq x \leq \frac{\pi}{6} \). **Instructions**: Keep your answer to 4 decimal places. --- **2. Volume of the Solid** Find the volume of the solid formed by revolving the region bounded by the graphs of: - \( y = x^2 + 1 \) - \( y = 0 \) - \( x = 0 \), and - \( x = 1 \) about the y-axis. **Instructions**: Keep your answer to 4 decimal places. --- These problems integrate topics of calculus including finding areas under curves and volumes of solids of revolution, suitable for students learning advanced integration techniques.
Transcribed Image Text:Certainly! Below is the transcription and explanation suited for an educational website: --- **Mathematics Problems** **1. Area of the Region** Find the area of the region between the functions: - \( f(x) = 6 \sin x \) - \( g(x) = 6 \cos 2x \) over the interval \( -\frac{\pi}{2} \leq x \leq \frac{\pi}{6} \). **Instructions**: Keep your answer to 4 decimal places. --- **2. Volume of the Solid** Find the volume of the solid formed by revolving the region bounded by the graphs of: - \( y = x^2 + 1 \) - \( y = 0 \) - \( x = 0 \), and - \( x = 1 \) about the y-axis. **Instructions**: Keep your answer to 4 decimal places. --- These problems integrate topics of calculus including finding areas under curves and volumes of solids of revolution, suitable for students learning advanced integration techniques.
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