A treatise on the integral calculus and its applications1857 |
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Page 20
... known form . √√ ( 1 ) sin " æde = - dx sin ̄1x ( 1 − x2 ) # 1 log x 3x3 6x2 3 This may be obtained by putting sinx = 0 . sin1x ( 1 − x2 ) - dx ( a2 — x2 ) § dx = tan + log cos 0 , where sin 0 = x . 31 . 1 cot Ꮎ 32 . = cot 0 + o ...
... known form . √√ ( 1 ) sin " æde = - dx sin ̄1x ( 1 − x2 ) # 1 log x 3x3 6x2 3 This may be obtained by putting sinx = 0 . sin1x ( 1 − x2 ) - dx ( a2 — x2 ) § dx = tan + log cos 0 , where sin 0 = x . 31 . 1 cot Ꮎ 32 . = cot 0 + o ...
Page 27
... known quantities , and P ' and Q ' involve the unknown quantities L and M to the first power only , so that we have two equations of the first degree for finding L and M. 23. To determine the partial fractions corresponding to a pair of ...
... known quantities , and P ' and Q ' involve the unknown quantities L and M to the first power only , so that we have two equations of the first degree for finding L and M. 23. To determine the partial fractions corresponding to a pair of ...
Page 48
... known as soon as we know the function ( x ) of which ( x ) is the differen- tial coefficient . In the pages immediately following we gave methods for finding ( x ) in different cases . We shall now add some miscellaneous remarks and ...
... known as soon as we know the function ( x ) of which ( x ) is the differen- tial coefficient . In the pages immediately following we gave methods for finding ( x ) in different cases . We shall now add some miscellaneous remarks and ...
Page 71
... known . dy in dx 69. The process of finding the length of a curve is called the rectification of the curve , because we may suppose the question to be this : Find a right line equal in length to any assigned portion of the curve . In ...
... known . dy in dx 69. The process of finding the length of a curve is called the rectification of the curve , because we may suppose the question to be this : Find a right line equal in length to any assigned portion of the curve . In ...
Page 72
... known if a certain integral can be obtained . It may happen in many cases that this integral cannot be obtained . Whenever the length of an arc of a curve can be expressed in terms of one or both of the co- ordinates of the variable ...
... known if a certain integral can be obtained . It may happen in many cases that this integral cannot be obtained . Whenever the length of an arc of a curve can be expressed in terms of one or both of the co- ordinates of the variable ...
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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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