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

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

Answer 1

[DGM]

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

Answer 2

[Yongjian Feng]

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?