calculus for engineers math 1110 -...
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![Page 1: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/1.jpg)
Dr. Mohamed Elshazly
CALCULUS FOR ENGINEERS MATH 1110
Instructor:Dr. Mohamed El-Shazly
Assistant Prof. of Mechanical Design and [email protected]
Office: S053
Faculty of EngineeringMechanical Engineering Department
![Page 2: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/2.jpg)
DOUBLE INTEGRALS
![Page 3: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/3.jpg)
![Page 4: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/4.jpg)
Example 1
![Page 5: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/5.jpg)
![Page 6: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/6.jpg)
![Page 7: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/7.jpg)
Example 2
![Page 8: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/8.jpg)
![Page 9: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/9.jpg)
![Page 10: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/10.jpg)
Example 3
![Page 11: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/11.jpg)
![Page 12: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/12.jpg)
Example 4
![Page 13: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/13.jpg)
![Page 14: CALCULUS FOR ENGINEERS MATH 1110 - KSUfac.ksu.edu.sa/sites/default/files/lecture-15-d-integral.pdf · 2014. 12. 8. · 0 y cos x5 dx dy = y cos x5 dA = o — cos x5 dx = cos x5 (5x4](https://reader033.vdocuments.net/reader033/viewer/2022060806/608b84b77272c224ec6b75ac/html5/thumbnails/14.jpg)
Example 5