Use the trapezium rule with four strips to find an estimate for
∫022x dx \int_0^2 2^x\,dx\,∫022xdx
Give your answer to four decimal places.
Given that ∫022x dx=3ln2\displaystyle\int_0^2 2^x\,dx = \frac{3}{\ln 2}∫022xdx=ln23, find the percentage error in the estimate found in part (a). Give your answer to two significant figures.
Explain, with reference to the shape of the curve y=2xy = 2^xy=2x, why the trapezium rule gives an overestimate here.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.