Question

If the shaded area region is A, estimate the value of the integral.

Answer 1

\[\int\limits_{-1.5}^{4} f(x)dx\]

Answer 2

Above is the image of the graph.

Answer 3

i would estimate a quadratic

Answer 4

f(x) = k(3-x)(5-x)

such that f(4) = -1

Answer 5

So then I should figure out what k is?

Answer 6

of course, since there are an infinite number of quadratics with those roots

k(3-4)(5-4) = -1

k(-1)(1) = -1, k = 1

Answer 7

Okay, and now how would I put that into the inergral?

Answer 8

*integral

Answer 9

define f(x) for that piece as: (3-x)(5-x) and integrate the poly

Answer 10

from 3 to 5 that is

Answer 11

Okay.
So then I have -2+2+((3-5)(5-5)-(3-3(5-3))

Answer 12

or the same area can be had from: x(2-x)

Answer 13

from 0 to 2

Answer 14

well, -x(2-x)

Answer 15

I am seeing zero as an answer.

Answer 16

x^2 - 2x, integrates to:

x^3/3 - x^2; at x=2 we have

8/3 - 4

(8-12)/3

Answer 17

I'm sorry. I'm a little lost.
Could you help me set up the entire integration over the interval?