1. ## Definite integrals

I need to express the area of the region as a definite integral.
f(x)=-x^(2)-2x+3

2. Originally Posted by nystudent2729
I need to express the area of the region as a definite integral.
f(x)=-x^(2)-2x+3

$\displaystyle \int_{a}^{b}{f(x)}dx = F(b) - F(a)$

where F is the antiderivative of f(x)

You need to give us the a and b so that we can tell you the area of the reagion.

For example if you want the area of a region of f(x)=-x^(2)-2x+3 from x=0 to x=6

$\displaystyle \int_{0}^{6}{(-x^{2}-2x+3)} dx$

3. ## Definite Integral

I need to express the area of the region from -3 to 1 as a definite integral:
f(x)=-x^(2)-2x+3

4. Originally Posted by nystudent2729
I need to express the area of the region from -3 to 1 as a definite integral:
f(x)=-x^(2)-2x+3
$\displaystyle \int_{-3}^{1}{(-x^{2}-2x+3) } dx$ = area of region

5. Dear nystudent2729,

you can easy check out that -3 and 1 is the roots of equation f(x) = 0. And f(x) > 0 in the given interval, therefore the area is the integral from -3 to 1.

This is elemtary integral, what is the problem?

6. Originally Posted by fonso_gfx
$\displaystyle \int_{a}^{b}{f(x)}dx = F(b) - F(a)$

where F is the antiderivative of f(x)

You need to give us the a and b so that we can tell you the area of the reagion.

For example if you want the area of a region of f(x)=-x^(2)-2x+3 from x=0 to x=6

$\displaystyle \int_{0}^{6}{(-x^{2}-2x+3)} dx$