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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6610 • Analysis of Numerical Methods I

Fall 2011 • Question 3

Question

Math 6610 • Analysis of Numerical Methods I Fall 2011 • Question 3
**Trapezoidal Rule** a) State the formula for the composite trapezoidal rule \(I_n(f)\) to approximate the integral \(I(f)=\int_a^b f(x)dx\) b) Bound the error in \(I_n(f)\) applied to the following integral: \[ \int_0^{\pi/2}\cos(x)dx \] (You do not need to derive the error formula.)

Raw LaTeX

{Trapezoidal Rule}

\partitem{a} State the formula for the composite trapezoidal rule \(I_n(f)\) to
approximate the integral \(I(f)=\int_a^b f(x)dx\)

\partitem{b} Bound the error in \(I_n(f)\) applied to the following integral:
\[
  \int_0^{\pi/2}\cos(x)dx
\]
(You do not need to derive the error formula.)

Topic Tags

Linear Programming and Optimization Numerical Quadrature Polynomial Interpolation and Error Formulas Quadrature Rules