13.2 Double Integrals over General Regions Problem 9 **9. Definition of Region R:**The region $ R $ is defined as follows:\[ R = \{(x, y) : 0 \leq x \leq \pi/4, \sin x \leq y \leq \cos x \} \]**Explanation:**- **Range for $ x $:** The variable $ x $ ranges from 0 to $\pi/4$.- **Range for $ y $:** For each value of $ x $, $ y $ is bounded between $\sin x$ and $\cos x$.This defines a region on the coordinate plane where $ x $ is between 0 and $\pi/4$, and for each $ x $, $ y $ is between the values of $\sin x$ and $\cos x$. **9–16. Regions of Integration**Sketch each region and write an iterated integral of a continuous function $ f $ over the region. Use the order $ dy \, dx $.

Given region, R=x,y : 0≤x≤π4, sinx≤y≤cosx Firstly, sketch the region.

Answered: 9-16. Regions of integration Sketch…

9-16. Regions of integration Sketch each region and write an iterated integral of a continuous function f over the region. Use the order dy dx.

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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Question

13.2 Double Integrals over General Regions Problem 9

**9. Definition of Region R:**

The region $ R $ is defined as follows:

\[ R = \{(x, y) : 0 \leq x \leq \pi/4, \sin x \leq y \leq \cos x \} \]

**Explanation:**

- **Range for $ x $:** The variable $ x $ ranges from 0 to $\pi/4$.
- **Range for $ y $:** For each value of $ x $, $ y $ is bounded between $\sin x$ and $\cos x$.

This defines a region on the coordinate plane where $ x $ is between 0 and $\pi/4$, and for each $ x $, $ y $ is between the values of $\sin x$ and $\cos x$.

**9–16. Regions of Integration**

Sketch each region and write an iterated integral of a continuous function $ f $ over the region. Use the order $ dy \, dx $.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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