Numerical approximation of elliptic integrals by quadrature rules

[3/100%]

Show

LaTeX

Show LaTeX

Problem 2.10.12 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Интегралы. Ряды." [ККЧ+03]More problems in Subsection 2.10.2 "Problems"

(1)(2)

Compute approximately, using Simpson's formula with $n = 4$ and $n = 8$ , the integral:

(1)

$\int_{0}^{\pi / 2} \sqrt{1-k^{2} \sin^{2} x} d x$ , if: а) $k^{2} = 0,5$ ; б) $k^{2} = 0,25$

(2)

$\int_{0}^{\pi / 2} \frac{d x}{\sqrt{1-k^{2} \sin^{2} x}}$ , if: а) $k = 0,5$ ; б) $k = 0,8$ ; в) $k = 0,9$ .

Problem 2.10.28 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Интегралы. Ряды." [ККЧ+03]More problems in Subsection 2.10.2 "Problems"

Compute the length of an ellipse with eccentricity $\varepsilon = 0,5$ and semi-axis $a = 1$ , using Simpson's formula with $n = 6$ . Estimate the error of the result.

Problem 2.10.29 from Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. "Интегралы. Ряды." [ККЧ+03]More problems in Subsection 2.10.2 "Problems"

Find approximately, with error not exceeding $5 \cdot 10^{-2}$ , the length of an ellipse with semi-axes $a = 10$ and $b = 6$ .

References

[ККЧ+03] Кудрявцев Л.Д., Кутасов А.Д., Чехлов В.И., Шабунин М.И. Интегралы. Ряды. 2-е изд., ФИЗМАТЛИТ, 2003.