Essentials of Calculus
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In our eReader you can find the full English version of the book. Read Essentials of Calculus Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Essentials of Calculus
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Ex. 4. Given dz = (3 .r- + 2 y-^)dx + (4 xy - 9 y^)dy.
Since — (3 ar- + 2 y-) = — (^4 .)-j/ — 9 y-) = iy, the differential is exact.
dy dx X-' + 2 xy-.
Integrating M dx with y constant, we have (.Vdx = j'(3 a;2 + 2 y-2)^,r -.
The part of -Y that does not contain .r is — 9 y-, and I — 9 y^ dy =— 3y^.
Therefore the integral is ^ = x" + 2xy- — Sy^ + C.
If Md.v + Xdy is an inexact differential, no function(j:. y) can be found the differentiation of which will pro ...duce this differential.
Consequently the integral I " {Md.v + Xdy) cannot be expressed as the dift'erence
What to read after Essentials of Calculus?
You can find similar books in the "Read Also" column, or choose other free books by E J Edgar Jerome Townsend to read online MoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Ex. 4. Given dz = (3 .r- + 2 y-^)dx + (4 xy - 9 y^)dy.
Since — (3 ar- + 2 y-) = — (^4 .)-j/ — 9 y-) = iy, the differential is exact.
dy dx X-' + 2 xy-.
Integrating M dx with y constant, we have (.Vdx = j'(3 a;2 + 2 y-2)^,r -.
The part of -Y that does not contain .r is — 9 y-, and I — 9 y^ dy =— 3y^.
Therefore the integral is ^ = x" + 2xy- — Sy^ + C.
If Md.v + Xdy is an inexact differential, no function
Consequently the integral I " {Md.v + Xdy) cannot be expressed as the dift'erence
What to read after Essentials of Calculus?
You can find similar books in the "Read Also" column, or choose other free books by E J Edgar Jerome Townsend to read online
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