"What is the strip width when $[a,b]$ is divided into $n$ equal strips?","back":"$h=\\dfrac{b-a}{n}$","points":1,"mcqOptions":null},{"id":"7499e923-d235-4d20-bcf0-d007f1a213e4","cardType":"basic","front":"How many ordinates are required for $n$ strips?","back":"$n+1$ ordinates","points":1,"mcqOptions":null},{"id":"d2691e3a-145b-49a5-b6d0-292208ba9150","cardType":"basic","front":"What coefficients are applied to successive ordinates in the composite trapezium rule?","back":"$1,\\ 2,\\ 2,\\ldots,\\ 2,\\ 1$","points":1,"mcqOptions":null},{"id":"d0d28230-f02c-4fc8-9298-66990376d7e2","cardType":"basic","front":"What is the trapezium-rule approximation over one strip of width $h$?","back":"$\\dfrac{h}{2}(y_0+y_1)$","points":1,"mcqOptions":null},{"id":"72a47dfe-d134-4527-811e-874b5ce79cfe","cardType":"basic","front":"State the composite trapezium rule for $n$ equal strips.","back":"$$\\int_a^b f(x)\\,dx\\approx\\frac{h}{2}\\left[y_0+y_n+2(y_1+\\cdots+y_{n-1})\\right]$$","points":1,"mcqOptions":null},{"id":"66a64b8b-03e3-416d-9627-14fc535861c4","cardType":"cloze","front":"A definite integral gives [ ] between the graph and the $x$-axis.","back":"A definite integral gives signed area between the graph and the $x$-axis.","points":null,"mcqOptions":null},{"id":"e1215459-81d9-4ecd-8418-ef47ddf983a4","cardType":"cloze","front":"Area below the $x$-axis contributes [ ] to a definite integral.","back":"Area below the $x$-axis contributes negatively to a definite integral.","points":null,"mcqOptions":null},{"id":"0781feea-1fa3-4e3b-ba73-e84a9bb4015c","cardType":"cloze","front":"The trapezium rule replaces each curved section with a straight [ ].","back":"The trapezium rule replaces each curved section with a straight chord.","points":null,"mcqOptions":null},{"id":"b26a175c-03cb-4659-9487-65b1ef4c6b4c","cardType":"basic","front":"When is the trapezium rule exact?","back":"When the graph is a straight line.","points":1,"mcqOptions":null},{"id":"798619da-56ee-4cac-ab96-a98ae5b50b1f","cardType":"basic","front":"Why is each interior ordinate multiplied by 2?","back":"It belongs to two neighbouring trapezia.","points":2,"mcqOptions":null},{"id":"a34485f9-c445-4b21-ac1e-af34a5771c75","cardType":"cloze","front":"Numerical integration uses numerical values and geometric shapes to [ ].","back":"Numerical integration uses numerical values and geometric shapes to approximate a definite integral.","points":null,"mcqOptions":null},{"id":"34574445-65d1-4e52-8911-104054a5c3cb","cardType":"basic","front":"Using one trapezium, what is the estimate for $\\int_1^3\\frac{1}{x}\\,dx$?","back":"$\\dfrac{4}{3}$","points":1,"mcqOptions":null},{"id":"a4f796c0-574c-4979-abcd-92b39880c124","cardType":"basic","front":"Using four equal strips, what is the trapezium-rule estimate for $\\int_0^2x^2\\,dx$?","back":"$2.75$","points":1,"mcqOptions":null},{"id":"6a41fb0f-a71e-4c25-a3ec-f95a50ba0305","cardType":"basic","front":"What quantity is obtained by integrating velocity with respect to time?","back":"Displacement","points":1,"mcqOptions":null},{"id":"9f56937b-367b-4af1-b1e6-2fba0539859a","cardType":"basic","front":"What displacement is estimated from velocities $3,5,8,9,7$ m s$^{-1}$ recorded every 2 s?","back":"$54$ m","points":1,"mcqOptions":null},{"id":"086eb4b1-94be-459a-abd4-1242cef3405a","cardType":"cloze","front

1.10.6 Trapezium rule (A-level only) Flashcards

1.10.6 Trapezium rule (A-level only) Flashcards