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.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.