Numerical Methods – Trapezium Rule - [Pure 3].

Question 1

What is the Trapezium Rule used for?

Answer 1

Finding the approximate area under the curve.

Question 2

What are the two type of curve names for graphs?

Answer 2

Concave and Convex.

Question 3

Is Convex an Over estimate or an Under estimate?

Answer 3

Over estimate.
(f’‘(x) > 0).

Question 4

Is Concave an Over estimate or an Under estimate?

Answer 4

Under estimate.
(f’‘(x) < 0).

Question 5

What is the difference between Strips and Ordinates?

Number of Strips = Number of Ordinates -1.

Answer 5

Strips are the rectangles of equal width and the ordinates are each of the individual lines.

Question 6

What is the equation for the Trapezium Rule?

Answer 6

^b∫_a y dx ≈ 1/2(h)[(y₀ + y_n) + 2(y₁ + y₂ + … + y_n-1)], where h = b-a/n.

Question 7

What is the letter ‘h’ for in the Trapezium Rule? How do you work it out?

Answer 7

The step.
* h = b-a/n, where n is the number of strips.

Question 8

How can you make the Trapezium Rule more accurate?

Answer 8

Add more strips/ ordinates.