Integral Approximation - Trapezium Rule Practice Problems Online

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

Find the approximate value of $\displaystyle{\int_0^{2} 7x^{3}dx}$ using the Trapezium rule, by dividing the interval into $4$ pieces.

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

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

\displaystyle{\frac{16}{n^{5}}\sum_{k=1}^{n}\left((k-1)^{4}+k^{4}\right)}

\displaystyle{\frac{16}{n^{5}}\sum_{k=1}^{n}k^{4}}

\displaystyle{\frac{16}{n^{5}}\sum_{k=0}^{n-1}k^{4}}

\displaystyle{\frac{16}{n^{5}}\sum_{k=0}^{n-1}\left((k-1)^{4}+k^{4}\right)}

Find the approximate value of $\displaystyle{\int_0^1 (12x^2+2)dx}$ using the Trapezium rule, by dividing the interval into $5$ parts.

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Integral Approximation - Trapezium Rule

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