Integration

Question 1

Given a function f, how can the area under the graph of y=f(x) between two x coordinates a and b be calculated?

Answer 1

∫f(x) dx, a to b

Question 2

How can ∫f’(x) dx, a to b be evaluated?

Answer 2

f(b)-f(a)

Question 3

Explain the trapezium rule of approximating ∫f(x) dx, a to b

Answer 3

The area is divided into n equal strips such that each strip has width w=(b-a)/n. Next, a value for f(x) is found for each value of x that forms a boundary at a strip, known as y₀, y₁, y₂,…,yᵣ. The area under the curve is approximately w(y₀+2(y₁+y₂+yᵣ₋₁)+yᵣ)/2