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Dr. Mohamed Elshazly CALCULUS FOR ENGINEERS MATH 1110 Instructor: Dr. Mohamed El-Shazly Assistant Prof. of Mechanical Design and Tribology [email protected] Office: S053 Faculty of Engineering Mechanical Engineering Department

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

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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

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

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
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

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
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
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

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
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
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

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
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

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
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

Example 5


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