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C4 Trapezium Rule

Using the trapezium rule with five equally spaced ordinates, find an approx value of:

[∫ between 4 and 2] 1/√(4x² - 9) dx

and

[∫ between 1 and -1] e^-2x dx

Thanks

Bloom
Reply 1
Avatar for RichE
RichE
15
what are you having a problem with - it amounts to put numbers into a formula :confused:
Reply 2
Avatar for oceane
oceane
10
For the first one:

it helps to draw the graph.
5 equally spaced x coordinates between 2 and 4 are: 2.0, 2.5, 3.0, 3.5, 4.0

You know the equation of the function so plug these values of x in to get:

x1=2 ---------------------------------- y1=0.34496
x2=2.5 ---------------------------------y2=0.25
x3=3.0----------------------------------y3=0.19245
x4=3.5----------------------------------y4=0.258114
x5=4.0----------------------------------y5=0.13484

area of trapezium = 1/2 (sum of parallel sides) * distance between them.
So:
area between x=2 and 2.5 = 1/2 (y1+y2) * 0.5= 0.15699
" " x=2.5 and 3 = 1/2 (y2+y3) * 0.5= 0.1106125
" " x=3 and 3.5 = 1/2 (y3+y4) * 0.5 = 0.087641
" " x=3.5 and 4 = 1/2 (y4+y5) * 0.5 = 0.073238

Add these all up to get 0.428
graph.bmp24.6KB

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