Approximate Integral of cos(x^2)

  • #1

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
 

Answers and Replies

  • #2
Ray Vickson
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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
 

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