Trapezoidal Rule Question - Integration (1 Viewer)

[reggie7]

Integration Questions

Simple question and I've forgotten how to answer it. Could someone please explain how to get:

Use the trapezoidal rule to find an approximation for:

1. 0∫2 (x^2 - x) dx, using 4 trapezia.

2. Evaluate: 4∫3 [(x^2 + x + 3) / (3x^5)]

3. Find the area enclosed between the curve y = (1/x^2), the y-axis and the lines y = 1 and y = 4 in the first quadrant.





Also do they ask these Trapezoidal and Simpson Rule questions in HSC exams or do they skip straight to primitive functions?

 

[steve001]

h = (2-0)/4
h =1/2

f(0)=0
f(0.5)=-0.25
f(1)= 0
f(1.5)=(0.75)
f(2)=2

A= (0.5)/2(0+2(-0.25+0+0.75)+2)
A=3/4 units squared

Is the second one using trapezoidial rule or just integration

You get either one trap question or one simpson rule question in the HSC

 

[reggie7]

Thanks, also posted a new question if yourself or anyone could answer please.

Also does "strips", "subintervals" & "trapezia" mean the same thing?

 

[steve001]

hey, for the second one i got 0.018 units^2 but i dint know if its right...i did it in that latex thing but i dont know how to put it here and yer they all mean the same thing

 

[x3.eddayyeeee]

Thanks, also posted a new question if yourself or anyone could answer please.

Also does "strips", "subintervals" & "trapezia" mean the same thing?

yes.
but dont get these mixed up with funtion values.