.pf{position:relative;background-color:#fff;overflow:hidden;margin:0;border:0}.pc{position:absolute;border:0;padding:0;margin:0;top:0;left:0;width:100%;height:100%;overflow:hidden;display:block;transform-origin:0 0;-ms-transform-origin:0 0;-webkit-transform-origin:0 0}.bi{position:absolute;border:0;margin:0}.c{position:absolute;border:0;padding:0;margin:0;overflow:hidden;display:block}.t{position:absolute;white-space:pre;font-size:1px;transform-origin:0 100%;-ms-transform-origin:0 100%;-webkit-transform-origin:0 100%;unicode-bidi:bidi-override;-moz-font-feature-settings:"liga" 0}.t:after{content:''}.t:before{content:'';display:inline-block}.t span{position:relative;unicode-bidi:bidi-override}._{display:inline-block;color:transparent;z-index:-1}.pi{display:none}@media screen{.pf{margin:13px auto;box-shadow:1px 1px 3px 1px #333;border-collapse:separate}}.ff1{font-family:ff1;line-height:.946289;font-style:normal;font-weight:400;visibility:visible}.ff2{font-family:ff2;line-height:.900879;font-style:normal;font-weight:400;visibility:visible}.m0{transform:matrix(.329965,0,0,.329965,0,0);-ms-transform:matrix(.329965,0,0,.329965,0,0);-webkit-transform:matrix(.329965,0,0,.329965,0,0)}.ls0{letter-spacing:0}.sc0{text-shadow:-.015em 0 transparent,0 .015em transparent,.015em 0 transparent,0 -.015em transparent}@media screen and (-webkit-min-device-pixel-ratio:0){.sc0{-webkit-text-stroke:.015em transparent;text-shadow:none}}.ws0{word-spacing:0}._0{margin-left:-1.036224px}.fc1{color:gray}.fc0{color:#000}.fs1{font-size:24.576px}.fs0{font-size:49.344px}.y4{bottom:2.256962px}.y2{bottom:4.408335px}.y0{bottom:48.834852px}.y3{bottom:1032.909923px}.y1{bottom:1045.804964px}.h4{height:9.946472px}.h5{height:18.66px}.h2{height:19.797913px}.h3{height:34.237219px}.h1{height:1017.612735px}.h0{height:1113.117868px}.w3{width:44.727445px}.w2{width:65.855778px}.w1{width:378.945256px}.w0{width:783.99736px}.x0{left:0}.x2{left:6.050242px}.x1{left:52.424874px}.x3{left:121.733408px}

MATH209 Lecture 14: Double Integrals and Iterated Integrals, Lecture 14

Canada

Calculus III

Mathematics

Venera Hrimiuc

University of Alberta

Introductory University Chemistry II

Mechanics of Deformable Bodies I

Fundamentals of Electrical Engineering

Computer Programming for Engineers

Engineering Economy

Mechanics

Technology and History

Calculus II

Applied Linear Algebra

Differential Equations

Advanced Boundary Value Problems I

Introductory Statistics for Engineering

Behavior in Organizations

Materials Science II

Introduction to Thermo-Fluid Sciences

Engineering Mechanics II

Mechanical Design I

Fluid Mechanics I

Applied Thermodynamics

Mechanical Design II

Mechanics of Machines

Numerical Methods of Mechanical Engineers

Fuel Cell Systems

<div style="font-family:'Helvetica Neue', Helvetica, Arial;color:#333333;"> <div> <br> <picture><source srcset="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/73/7315222.jpeg" type="image/webp"></source><img src="https://prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/73/7315222.jpeg" alt=""></picture> </div> </div> <div id="ajj" class="hidden">15.1 Double and Iterated Integrals over Rectangles Objective: Evaluate double integrals over rectang X) 15.1.15 Evaluate the double integral over the given region R. </div> <div class="avatar-comments hide"><div class="comment-box"> <div class="comments-header">Comments</div> <ul class="comments-list"></ul> <div class="leave-comment "></div> </div></div>

<p>In evaluating a double integral over a region <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/0.webp?img=710ab96d098c17fc671e5f0e1ce945ec" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/0.png?img=310d1ad1575fa1b1854245e9f7cc958e" data-mlang="latex" data-equation="D"></picture><em>,</em> a sum of iterated integrals was obtained as follows</p>
<p><picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/0.webp?img=172a4fdc9abd99fa7ab90377f0bfc1ff" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/0.png?img=cae68681402ca92fba25d5cd2665604e" data-mlang="latex" data-equation="%5Ciint%5Climits_%7BD%7Df(x%2Cy)dA%3D%5Cint_%7B0%7D%5E%7B1%7D%5Cint_%7B0%7D%5E%7B2y%7Df(x%2Cy)dxdy%2B%5Cint_%7B1%7D%5E%7B3%7D%5Cint_%7B0%7D%5E%7B3-y%7Df(x%2Cy)dxdy"></picture>    </p>
<p>Sketch the region <picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/2.webp?img=f5373da14d590d9a74d9ab7c911f8f2b" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/961293871061285/question/2.png?img=d7527d8ba68596a0e147824e6a9121d5" data-mlang="latex" data-equation="D"></picture><em> </em>and express the double iterated integral as an iterated integral with reversed order of integration.</p>
<p> </p>

<p>When evaluating the given double integral, a sum of iterated integrals was obtained as follows:</p>
<p><picture><source srcset="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/590276728849216/question/0.webp?img=7fb82ddcf58070967e68ad5db0cb9b70" type="image/webp"><img src="https://s3.amazonaws.com/prealliance-textbook-qa.oneclass.com/qa_images/homework_help/question/qa_images/590276728849216/question/0.png?img=a3f39a74f2ba511ae8936ae94ff4d264" data-mlang="latex" data-equation="%5Cint%20%5Cint%20_D%5C%3Af%5Cleft(x%2Cy%5Cright)dA%5C%3A%3D%5Cint%20_0%5E1%5Cint%20_0%5E%7B2y%7D%5C%3Af%5Cleft(x%2Cy%5Cright)dxdy%2B%5Cint%20_1%5E3%5Cint%20_0%5E%7B3-y%7D%5C%3Af%5Cleft(x%2Cy%5Cright)dxdy"></picture>  </p>
<p>Sketch the region D and express the double integral as an iterated integral with reversed order of integration.</p>

MATH209 Lecture Notes - Lecture 20: Victorian Railways Z Type Carriage, Iterated Integral, Paga

MATH209 Lecture Notes - Lecture 21: Multiple Integral, Mue, Victorian Railways Z Type Carriage

MATH209 Lecture 14: Double Integrals and Iterated Integrals, Lecture 14

Get access

Related textbook solutions

Calculus

Single Variable Calculus: Early Transcendentals

CALCULUS:EARLY TRANSCENDENTALS

Related Documents

MATH209 Lecture Notes - Lecture 20: Victorian Railways Z Type Carriage, Iterated Integral, Paga

MATH209 Lecture Notes - Lecture 21: Multiple Integral, Mue, Victorian Railways Z Type Carriage

MATH209 Lecture 19: Application of Double Integrals, Lecture 19

Related Questions