"INTEGRATION, ARC LENGTH (CIRCUMFERENCE) OF ELLIPSE. The arc length or circumference of an ellipse can be written using an elliptic integral of the second kind E(k,Φ): ■ L = 4 * a * E pi/2 2 2 E(k,Φ) = ƒ sqr( 1 - K * sin (Φ) δ Φ, k = sqr (a^2 +b^2)/a 0 ■ where a and b are 1/2 the lengths of the two principal axes. The integration is over the range Φ = 0 to pi/2. (c) Copyright PCSCC, Inc., 1993*** Answer(s) to problem *** Type F then I to inactivate variable K. Integration is on Φ which is active. Set A=50 and B=10. Move cursor to Φ. Type G. For the range on integrand Φ type, (end esc) 0 to 1.5707963 (enter). The circumference is approximately 210.0686. Type any key to stop integration after SIG FIGS is greater than 10. ||Estimate the circumference of an ellipse with axes lengths of 50 and 10 cm as measured from its origin. Use the elliptic integral method. Type comma key to see answer. Type (F2) to return to application file."
