Practice Question: Trapezoid Rule Approximation

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Wize University Calculus 2 Textbook > Integration Techniques

Numerical Integration

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Practice Question
Given the integral ∫0πsin⁡(x2)dx{\displaystyle \int^{\sqrt{\pi}}_0}\sin\left(x^2\right)dx∫0π​​sin(x2)dx,
a) find the approximation for using the Trapezoid rule with n=2n=2n=2.
b) estimate the error in the approximation you found.
c) what is the minimum nnn value required to guarantee that the approximation is accurate within 0.0001?

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More Numerical Integration Questions:

The Trapezoid Rule

Approximate ∫151+x2 dx\displaystyle\int\limits_{1}^{5}\sqrt{1+x^{2}}\,dx1∫5​1+x2​dx  using the Trapezoidal Rule with n=8n=8n=8 (answer correct to 2 decimal places).
 