A treatise on the integral calculus and its applications1857 |
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Page 25
... contain the factor x- - φ ( 2 ) A F ( x ) = x - a a once ; assume + where A is a constant , and X ( x ) f ( x ) the partial fractions exclusive of From ( 1 ) X ( x ) ( x ) A ............ . ( 1 ) , represents the sum of all x - a " and F ...
... contain the factor x- - φ ( 2 ) A F ( x ) = x - a a once ; assume + where A is a constant , and X ( x ) f ( x ) the partial fractions exclusive of From ( 1 ) X ( x ) ( x ) A ............ . ( 1 ) , represents the sum of all x - a " and F ...
Page 55
... contained in the formula ( 4n - 1 ) , where n is any integer . Suppose we take the value ( 4n - 1 ) , where n is some definite integer , then corresponding to the value x = a we must take 0 = ( 4n - π 1 ) ; this will be obvious on 2 ...
... contained in the formula ( 4n - 1 ) , where n is any integer . Suppose we take the value ( 4n - 1 ) , where n is some definite integer , then corresponding to the value x = a we must take 0 = ( 4n - π 1 ) ; this will be obvious on 2 ...
Page 66
... contain y , but may contain x ; we may denote it by x ( x ) . And [ f ( y ) dy we will denote by ( y ) ; thus finally d'u v = ¥ ( y ) + x ( x ) . Therefore two values of u which satisfy the equation ( x , y ) can only differ by the sum ...
... contain y , but may contain x ; we may denote it by x ( x ) . And [ f ( y ) dy we will denote by ( y ) ; thus finally d'u v = ¥ ( y ) + x ( x ) . Therefore two values of u which satisfy the equation ( x , y ) can only differ by the sum ...
Page 105
... . ( y ) , 134. If a curve be determined by the equation x = then the area contained between the curve , the axis of y , and lines drawn parallel to the axis of x at distances AREAS OF PLANE CURVES AND OF SURFACES . 105.
... . ( y ) , 134. If a curve be determined by the equation x = then the area contained between the curve , the axis of y , and lines drawn parallel to the axis of x at distances AREAS OF PLANE CURVES AND OF SURFACES . 105.
Page 106
... contained between the curve y = c sin , the axis of a , and ordinates at the distances X1 and x , respectively from the axis of y . We have a x2 sin 1 Ꮖ dx = = ca a ( cos 24 - COS 8 252 ) . Suppose then x1 = COS a O and x = απ ; the ...
... contained between the curve y = c sin , the axis of a , and ordinates at the distances X1 and x , respectively from the axis of y . We have a x2 sin 1 Ꮖ dx = = ca a ( cos 24 - COS 8 252 ) . Suppose then x1 = COS a O and x = απ ; the ...
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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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