A treatise on the integral calculus and its applications1857 |
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... quantity PAGE I 22 38 48 64 ΤΙ 103 142 which it may involve 165 X. Elliptic Integrals 174 XI . Change of the Variables in a Multiple Integral 180 XII . Definite Integrals 212 XIII . Expansion of Functions in Trigonometrical Series 250 ...
... quantity PAGE I 22 38 48 64 ΤΙ 103 142 which it may involve 165 X. Elliptic Integrals 174 XI . Change of the Variables in a Multiple Integral 180 XII . Definite Integrals 212 XIII . Expansion of Functions in Trigonometrical Series 250 ...
Page 2
... quantity . For let A denote the numerically greatest value which ( x ) can have when x lies between a and b ; then ... quantities P1 , P2 , ... P ; hence Zho ultimately vanishes , and we obtain this result - the limit of Σ ( x ) Ax when ...
... quantity . For let A denote the numerically greatest value which ( x ) can have when x lies between a and b ; then ... quantities P1 , P2 , ... P ; hence Zho ultimately vanishes , and we obtain this result - the limit of Σ ( x ) Ax when ...
Page 3
... quantities ultimately vanishes . 6. The above process is called Integration ; the quantity f ( x ) dx is called a definite integral , and a and b are called a ф the limits of the integral . Since the value of this definite integral is ...
... quantities ultimately vanishes . 6. The above process is called Integration ; the quantity f ( x ) dx is called a definite integral , and a and b are called a ф the limits of the integral . Since the value of this definite integral is ...
Page 5
... quantity ; hence if ( x ) be a function having ( x ) for its differential coeffi- cient , then ( x ) + C , where C is any quantity independent of X , is the only form that can have the same differential coefficient . Hence , hereafter ...
... quantity ; hence if ( x ) be a function having ( x ) for its differential coeffi- cient , then ( x ) + C , where C is any quantity independent of X , is the only form that can have the same differential coefficient . Hence , hereafter ...
Page 11
... quantity dx Ex . ( 6 ) . √ √ ( a + bx - cx2o ) Iva dx √ ( a + bx − cx2 ) 1 bxc - ca " ) = √c 4c2 = dx bx + 1 с - log 2c . Ne dx b ---- ( -- ) and z for x - h 2c ' ( 4ac + b2 4c2 x 2c / thus the integral be- 4ac + b2 Put h2 for dz ...
... quantity dx Ex . ( 6 ) . √ √ ( a + bx - cx2o ) Iva dx √ ( a + bx − cx2 ) 1 bxc - ca " ) = √c 4c2 = dx bx + 1 с - log 2c . Ne dx b ---- ( -- ) and z for x - h 2c ' ( 4ac + b2 4c2 x 2c / thus the integral be- 4ac + b2 Put h2 for dz ...
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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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