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Numerical_Integration

# Numerical_Integration - R 4 xe 2 x dx Calculate the exact...

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MAT 2384-Practice Problems on Numerical Integration Methods 1. Use the rectangular rule to estimate the value of R 0 . 5 0 cos( x 2 ) dx within 0 . 01 2. Use the rectangular rule to estimate the value of R 2 0 xe - x 2 dx within 0 . 01. Compute the exact value of the integral and compare with your estimate by the Rectangular Rule. 3. Using the Trapezoidal Rule, compute the value of R 1 0 4 1+ x 2 accurate within 0.001. Use your answer to give an estimation of the value of π accurate to three decimal places. 4. Repeat Problem (3) using the Simpson’s Rule with an accuracy of 0 . 0001 5. Use Simpson’s rule with n = 8 subdivisions to estimate the value of R 2 1 e x ln( x ) dx . Give an upper bound for the Error 6. Use the two-points Gauss Quadrature Rule to compute the value of
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Unformatted text preview: R 4 xe 2 x dx . Calculate the exact value of the integral to deduce the Error. 7. Use the Gaussian Quadrature Rule of order 4 (Four-Points Gauss Quadrature Rule) to compute the value of R 2 1 √ 1+ x 2 x dx . 8. Use the Gaussian Quadrature Rule of order 5 (Five-Points Gauss Quadrature Rule) to compute the value of R 1 . 5 1 x 2 ln( x ) dx . Compute the exact value of the integral and give the error. 9. Use Simpson’s rule with n = 8 subdivisions to estimate the value of R 2 1 x 2 e x 2 ln( x ) dx . Give bounds for the error on your estimation. 1...
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