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Numerical Approximation of Integrals

Integral Approximation - Trapezium Rule


The following is Devin's approximation of an integral using the Trapezium rule: 65(0+2(35)5+2(65)5+2(95)5+2(125)5+(155)5).\frac{6}{5}\cdot\left(0 + 2\cdot\left(\frac{3}{5}\right)^{5}+2\cdot\left(\frac{6}{5}\right)^{5}+2\cdot\left(\frac{9}{5}\right)^{5}+2\cdot\left(\frac{12}{5}\right)^{5}+\left(\frac{15}{5}\right)^{5}\right). Which of the following integrals is Devin approximating?

Find the approximate value of 027x3dx\displaystyle{\int_0^{2} 7x^{3}dx} using the Trapezium rule, by dividing the interval into 44 pieces.

What is the Trapezium rule approximation to the definite integral 11(102x2)dx\displaystyle{\int_{-1}^1 (10-2x^2)dx} using four intervals?

Which of the following represents the approximation of 02x4dx\displaystyle{\int_{0}^{2}x^{4}dx} using the Trapezium rule?

Find the approximate value of 01(12x2+2)dx\displaystyle{\int_0^1 (12x^2+2)dx} using the Trapezium rule, by dividing the interval into 55 parts.


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