Question

Algebra 2 help please??!

Evaluate the area under g(x) = –x2 – 3x + 7 for –4 ≤ x ≤ 1.

A.35.58 units^2
B.44.64 units^2
C.35.83 repeating units^2
D.none of these

Answer 1

Do you know how to integrate between limits?

Answer 2

so \[Area = \int\limits_{-4}^{1} (–x ^{2} – 3x + 7) dx\]

Answer 3

no, honesty, I just don't get this

Answer 4

that didn't help.. anyone else?

Answer 5

Have you seen integration before at all? If you have I can talk you through it, but if not then I obviously can't

Answer 6

ya, im looking at the lesson rite now.. im still confused?

Answer 7

okay so i can explain integration to you...
the whole purpose of integrating a function is to find the area underneath a curve.
so you're given g(x) = –x^2 – 3x + 7
which looks a bit like this

so in order to find the area underneath the curve (ie the lined bit) we have to integrate the formula of the curve

so if we have a function \[\int\limits_{?}^{?}x ^{n}dx = \frac{ x ^{n+1} }{ n+1 }\]
so if we integrate
g(x)=–x^2 – 3x + 7
we have to increase the powers by 1, and divide by the new power so
\[\int\limits_{-1}^{4} (–x^2 – 3x + 7) dx = \frac{ -x ^{3} }{ 3 }-\frac{ 3x ^{2} }{ 2 }+7x\]
then you have to substitute in your x=4 then also work out x=-1 and subtract one from the other