A Treatise On the Integral Calculus And Its Applications With Numerous Examples
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The area between the tractory, the axis of y, and the asymptote is -t~ . (See Ai't. 100, and Ai't. 134. ) 1-i. Find the area of a loop of the curve i/~ (a* + cc") = a;- (a^ — x^). Result -^ (tt - 2).
15. Find the area of the loop of the curve 16aV = Z>V (a^ — 2ax). • Result.
^ ^ ^ SO IG. Find the area of the loop of the curve 2f {a' + x') = {a' - xy-.
Result, a" [S V2 log (1 + V2) - 2}.
17. Find the whole area of the curve 2if {a? + x") - ^ay (a' - x") + (a' - xj = 0.
Result. AV •] 4 ^— Y .
18.... Find the area of the curve y = c sin - . Lofj sin - from ic — to a; = air. Result. 2ac (1 — log 2).
19. Find the area of the curve -= (-) between x = a and c V«/ X = /3, and /ro??i tJi5 result deduce the area of the hyperbola xy = a* betvyeen the same limits.
20. Find the area of the ellipse whose equation is ax~ + 2hxy + cy" = 1. Result.
TT »J{ac — y^) ' 21. Find the area of a loop of the curve r^ = a^ cos 29.
Result. -^.
T. I. C. 11 1G2 EXAMPLES.
22. Find the area contained by all the loops of the curve r = a sin nd.
What to read after A Treatise On the Integral Calculus And Its Applications With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The area between the tractory, the axis of y, and the asymptote is -t~ . (See Ai't. 100, and Ai't. 134. ) 1-i. Find the area of a loop of the curve i/~ (a* + cc") = a;- (a^ — x^). Result -^ (tt - 2).
15. Find the area of the loop of the curve 16aV = Z>V (a^ — 2ax). • Result.
^ ^ ^ SO IG. Find the area of the loop of the curve 2f {a' + x') = {a' - xy-.
Result, a" [S V2 log (1 + V2) - 2}.
17. Find the whole area of the curve 2if {a? + x") - ^ay (a' - x") + (a' - xj = 0.
Result. AV •] 4 ^— Y .
18.... Find the area of the curve y = c sin - . Lofj sin - from ic — to a; = air. Result. 2ac (1 — log 2).
19. Find the area of the curve -= (-) between x = a and c V«/ X = /3, and /ro??i tJi5 result deduce the area of the hyperbola xy = a* betvyeen the same limits.
20. Find the area of the ellipse whose equation is ax~ + 2hxy + cy" = 1. Result.
TT »J{ac — y^) ' 21. Find the area of a loop of the curve r^ = a^ cos 29.
Result. -^.
T. I. C. 11 1G2 EXAMPLES.
22. Find the area contained by all the loops of the curve r = a sin nd.
What to read after A Treatise On the Integral Calculus And Its Applications With Numerous Examples?
You can find similar books in the "Read Also" column, or choose other free books by Todhunter, I. (Isaac), 1820-1884 to read onlineMoreLess
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