I don't know how to write the following problem: f(x)=2x^3-​15.4x^2+2.​7x+2.25 - Determine the area under f(x) on the interval [-1,8]. Use the zeros rounded to one decimal

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f(x)=2x^3-15.4x^2+2.7x+2.25 - Determine the area under f(x) on the interval [-1,8]. Use the zeros rounded to one decimal.
zero points are: x=-0.3, x=0.5, x=7.5

Answers (2)

DGM
DGM on 30 Nov 2021
This can all be done symbolically easily enough
xrange = [-1 8];
syms x
f = 2*x^3 - 15.4*x^2 + 2.7*x + 2.25;
area = int(f,x,xrange)
area = 
double(area)
ans = -480.6000
fplot(f,xrange)
grid on
but why would the zeros be needed? Is that just a confusing way of saying "integrate abs(f)"?
absarea = int(abs(f),x,xrange)
absarea = 
double(absarea)
ans = 512.9550

Yongjian Feng
Yongjian Feng on 30 Nov 2021
Area under f(x) basically is just the definite integral of f(x) within the range, right?
You know how to use matlab to do integration?

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