A253300 Decimal expansion of integral_{x=0..1} x^sqrt(x) dx.

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

Offset: 0

Author

Jean-François Alcover, Dec 30 2014

Keywords

• nonn
• cons
• easy

Examples

			0.6585823541090935654696568534036441701564...
		

References

• Paul J. Nahin, Inside Interesting Integrals, Springer 2014, ISBN 978-1493912766.

Links

• Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (6.1.6)

Crossrefs

Cf. A073009, A083648, A253299.

Programs

Mathematica

NIntegrate[x^Sqrt[x], {x, 0, 1}, WorkingPrecision -> 110] // RealDigits[#, 10, 105]& // First

PARI

intnum(x=0,1, x^sqrt(x)) \\ Michel Marcus, Dec 30 2014

Formula

Equals sum_{n >= 1} (-1)^(n + 1)*(2/(n + 1))^n.