## A treatise on the integral calculus and its applications1857 |

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**Double Integration**VI . Lengths of Curves . VII . Areas of Plane Curves and of Surfaces VIII . Volumes of Solids IX . Differentiation of an Integral with respect to any quantity PAGE I 22 38 48 64 ΤΙ 103 142 which it may involve 165 X ... Page 63

... constant , ( a2 + c2 ) $ where tan 6 = 2 . Hence shew that if e cos ax be - α с integrated n times successively the result is ex cos ( ax - no ) ( a2 + c2 ) n 64 CHAPTER V.

... constant , ( a2 + c2 ) $ where tan 6 = 2 . Hence shew that if e cos ax be - α с integrated n times successively the result is ex cos ( ax - no ) ( a2 + c2 ) n 64 CHAPTER V.

**DOUBLE INTEGRATION**. 56. LET ( x MISCELLANEOUS EXAMPLES . 63. Page 64

Isaac Todhunter. 64 CHAPTER V.

Isaac Todhunter. 64 CHAPTER V.

**DOUBLE INTEGRATION**. 56. LET ( x ) denote any function of x ; then we have seen that the integral of ( x ) is a quantity u such that ( x ) . The integral may also be regarded as the limit du dx = of a ... Page 65

... integrate ( x , y ) with respect to y , and then integrate the result with respect to x . The above expression for u may be more concisely written thus dx [ f ( x , y ) dy de , or f ( x , y ) da dy . On this point ...

... integrate ( x , y ) with respect to y , and then integrate the result with respect to x . The above expression for u may be more concisely written thus dx [ f ( x , y ) dy de , or f ( x , y ) da dy . On this point ...

**DOUBLE INTEGRATION**. 65. Page 66

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**double integration**and summation . Let ( x , y ) be a function of x and y , which remains finite and continuous so long as x lies between the fixed values a and b , and y between the fixed values a and B. Let a , x ...**DOUBLE INTEGRATION**.### Other editions - View all

### Common terms and phrases

Application c² sin² Cambridge circle cloth co-ordinates constant cos² cos³ Crown 8vo curve cycloid definite integral denote differential coefficient double integral dx dx dx dy dz dy dx dz dx element ellipse equal Eulerian integral example expression Fcap Fellow of St Find the area find the volume formula function Hence indefinitely Integral Calculus integrate with respect intrinsic equation John's College latus rectum length limits M.A. Fellow MACMILLAN & CO.'S numerous obtain ordinate parabola partial fractions perpendicular plane positive preceding article radius vector result revolution revolve round round the axis shew sin² solid suppose surface tangent tion tractory transformed integral Trinity College unity vanishes variables vertex x₁ Y₁ πα аф

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