Posted by **aimee** on Friday, February 12, 2010 at 1:24pm.

Consider the following shaded region.

Find the area S of this region if a = 6, b = 3. (Give an exact answer.)

The two graphs intercept at 0 and the other limit is not given. The integral is int(ax-x^2)-(bx. So y=ax+x^2 is the graph on top and y=bx is at the bottom.

- calculus -
**drwls**, Friday, February 12, 2010 at 1:35pm
The upper limit of the integration will be where the curves intersect.

That is where 6x - x^2 = 3x.

x^2 -3x = x(x-3) = 0

x = 0 or 3

Now calculate

int(6x-x^2)-(3x)dx from 0 to 3

= int 3x - x^2 dx from 0 to 3

= [3x^2/2 - x^3/3]@x=3 - 0

(Since the value of the indefinite integral in brackets, at x = 0, is 0)

= 27/2 - 27/3 = 27/6 = 9/2

## Answer this Question

## Related Questions

- calculus - 1. Find the area of the region bounded by f(x)=x^2 +6x+9 and g(x)=5(x...
- calculus - Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...
- statistics finding the shaded region - Find the area of the shaded region. The ...
- calculus - 3). The shaded region is bounded by the y-axis and the graphs of y=1...
- math, calculus - 1. Consider the region bounded by the curves y=|x^2+x-12|, x=-5...
- Calculus - Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2...
- calculus - 1. Let R be the region in the first quadrant enclosed by the graphs ...
- calculus - Sketch the region enclosed by the given curves. Decide whether to ...
- calculus - could some body please check this for me? 1. find the exact ...
- Math - A man owns a rectangular piece of land. The land is divided into four ...

More Related Questions