How large should n be to guarantee the Trapezoidal Rule/Midpoint Rule/Simpson's Rule approximation for the integral 0 to pi/2 of sqr(cosx) dx be accurate to within 0.000001?
To find n, I know I need to use the error bound formula for the trapezoidal, midpoint, or simpson's rule. I found the second derivative to be:
-(sin^2x+2cos^2x)/(4cosx(sqrt(cosx)))
I also found the fourth derivative to be:
(15(sin^4x)+20cos^2xsin^2x + 4(cos^4x))/(16(sqrt(cos^7x))).
I know that a=0, b=pi/2, E=0.000001, and K is max when x=pi/2, but when I plug x into each of the equations, 0 is in the denominator. How can I find K?
To find n, I know I need to use the error bound formula for the trapezoidal, midpoint, or simpson's rule. I found the second derivative to be:
-(sin^2x+2cos^2x)/(4cosx(sqrt(cosx)))
I also found the fourth derivative to be:
(15(sin^4x)+20cos^2xsin^2x + 4(cos^4x))/(16(sqrt(cos^7x))).
I know that a=0, b=pi/2, E=0.000001, and K is max when x=pi/2, but when I plug x into each of the equations, 0 is in the denominator. How can I find K?