Approximate Integral of cos(x^2)

[sugarxsweet]

Homework Statement

I am having issues figuring out the error involved in the trapezoidal and midpoint methods for ∫cos(x^2) from 0 to 1 with n=8

Homework Equations

|Et|<= k(b-a)^3/(12n^2)
|Em|<=k(b-a)^3/(24n^2)

The Attempt at a Solution

f(x)=cos(x^2)
f'(x)=-2xsin(x^2)
f''(x)=-4x^2cos(x^2)

f''(1) = -3.844

Is it right given that f''(1) is negative? Just wanted to make sure! Thanks

 

[Ray Vickson]

Homework Statement

I am having issues figuring out the error involved in the trapezoidal and midpoint methods for ∫cos(x^2) from 0 to 1 with n=8

Homework Equations

|Et|<= k(b-a)^3/(12n^2)
|Em|<=k(b-a)^3/(24n^2)

The Attempt at a Solution

f(x)=cos(x^2)
f'(x)=-2xsin(x^2)
f''(x)=-4x^2cos(x^2)

f''(1) = -3.844

Is it right given that f''(1) is negative? Just wanted to make sure! Thanks

It doesn't matter: k = max{|f''(x)|: 0 ≤ x ≤ 1}.

RGV