A treatise on the integral calculus and its applications1857 |
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... lengths and areas of curves and of the volumes of solids , and an attempt has been made to explain those difficulties which usually perplex beginners — especially with reference to the limits of integrations . The transformation of ...
... lengths and areas of curves and of the volumes of solids , and an attempt has been made to explain those difficulties which usually perplex beginners — especially with reference to the limits of integrations . The transformation of ...
Page
... 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. Elliptic Integrals 174 ...
... 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. Elliptic Integrals 174 ...
Page 70
... x and y ; and 7 , and 7 , may be functions of x . This triple integral is the limit of a certain series which may be denoted by Zo ( x , y , z ) Ax △ y Az . no 71 CHAPTER VI . LENGTHS OF CURVES . Plane Curves 70 DOUBLE INTEGRATION .
... x and y ; and 7 , and 7 , may be functions of x . This triple integral is the limit of a certain series which may be denoted by Zo ( x , y , z ) Ax △ y Az . no 71 CHAPTER VI . LENGTHS OF CURVES . Plane Curves 70 DOUBLE INTEGRATION .
Page 71
... length of the arc AP measured from a fixed point A up to P ; T M R then , ( Dif . Cal . Art . 307 ) Hence , ds dx = dy / { 1 + ( d ) " } . dy dx == √√√ { 1+ ( 3/4 ) " } dar . S = From the equation to ... length Lengths of Curves ΤΙ.
... length of the arc AP measured from a fixed point A up to P ; T M R then , ( Dif . Cal . Art . 307 ) Hence , ds dx = dy / { 1 + ( d ) " } . dy dx == √√√ { 1+ ( 3/4 ) " } dar . S = From the equation to ... length Lengths of Curves ΤΙ.
Page 72
... length of an arc of a curve can be expressed in terms of one or both of the co- ordinates of the variable extremity of the arc , the curve is said to be rectifiable . 70. Application to the ... length of the 72 LENGTHS OF CURVES .
... length of an arc of a curve can be expressed in terms of one or both of the co- ordinates of the variable extremity of the arc , the curve is said to be rectifiable . 70. Application to the ... length of the 72 LENGTHS OF CURVES .
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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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