A103713 Decimal expansion of the area of the surface generated by revolving about the y-axis that part of the curve y = log x lying in the 4th quadrant.

7, 2, 1, 1, 7, 9, 9, 7, 2, 4, 2, 0, 7, 0, 4, 6, 9, 6, 4, 6, 8, 7, 7, 3, 2, 7, 6, 9, 8, 0, 0, 6, 6, 7, 6, 7, 9, 0, 2, 7, 0, 5, 7, 6, 1, 7, 9, 7, 6, 0, 5, 0, 0, 6, 4, 6, 0, 8, 8, 2, 6, 7, 4, 6, 1, 3, 1, 3, 0, 3, 6, 4, 8, 6, 1, 0, 9, 7, 6, 9, 6, 5, 1, 4, 6, 2, 1, 9, 2, 1, 0, 9, 7, 7, 6, 9, 8, 2, 9, 3, 2, 9, 9, 3, 4

Offset: 1

Author

Sylvester Reese and Jonathan Sondow, Feb 21 2005

Keywords

• cons
• easy
• nonn

Comments

Equal to Pi times its analog for the parabola (see A103710).

Examples

			7.21179972420704696468773276980066767902705761797605...
		

References

• C. E. Love, Differential and Integral Calculus, 4th ed., Macmillan, 1950, p. 288.
• S. Reese, A universal parabolic constant, 2004, preprint.

Links

• S. R. Finch, Mathematical Constants, addenda, sec. 8.1
• S. Reese, Pohle Colloquium Video Lecture: The universal parabolic constant, February 2, 2005
• S. Reese and J. Sondow, MathWorld: Universal Parabolic Constant
• Wikipedia, Universal parabolic constant

Crossrefs

Cf. A000796*A103710. See also A103714.

Programs

Mathematica

RealDigits[Pi*(Sqrt[2]+Log[1+Sqrt[2]]),10,120][[1]] (* or *) RealDigits[Pi* (Sqrt[2]+ArcSinh[1]),10,120][[1]] (* Harvey P. Dale, May 02 2011 *)

PARI

Pi*(sqrt(2) + log(1 + sqrt(2))) \\ Michel Marcus, Jul 06 2015

Formula

Pi*(sqrt(2) + log(1 + sqrt(2))).