Trapezium Rule (Numerical Integration) (AQA A-Level Mathematics): Quizzes

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Trapezium Rule (Numerical Integration)
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When rectangle tops lie above a curve, what type of estimate do they give?

Overestimate

When rectangle tops lie beneath a curve, what type of bound is produced?

Lower bound

What is the upper bound for ∫05x2dx\int_0^5 x^2 dx using rectangles with width 1?

55

What is the lower bound for ∫05x2dx\int_0^5 x^2 dx using left rectangles with width 1?

30

How many ordinates are needed for 5 strips in the trapezium rule?

6

How can you improve the estimate given by the trapezium rule?

Use more/thinner strips

Why do trapeziums overestimate positive convex curves?

Tops lie above the curve

What does hh represent in the trapezium rule formula?

Width of each strip

What is ∫abf(x)dx\int_a^b f(x) dx the limit of as h→0h \rightarrow 0?

Rectangle approximation

Using trapezium rule with h=1h=1 for y=x2y=x^2 from 0 to 5, what is the result?

852\frac{85}{2}

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