Question 1 of 4Numerical integration, integration by parts, Newton-Raphson
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Use the trapezium rule with 5 ordinates (h=0.25) to find an approximate value of \displaystyle\int_0^1x^2e^x\,dx, to 2 d.p.
Evaluate the exact value of \displaystyle\int_0^1x^2e^x\,dx using integration by parts.
The trapezium rule gives 0.76 for \int_0^1x^2e^x\,dx, whose exact value is e-2\approx0.718. Is this an over-estimation or under-estimation,…
Use the Newton-Raphson method, starting from x_0=1, to find a root of x^3+3x-7=0, correct to 2 d.p.
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