# Area of the region?

• May 12th 2009, 05:41 AM
Calculusretard
Area of the region?
guuh, I've been working on this problem forever and can't get it.

Find the area of the region bounded by the graphs f(x) = -x^2 + 7x + 20 and g(x) = x^2 + 5x - 40

To get the left and right x values

I do f(x) = g(x)

x^2 + 7x + 20 = x^2 + 5x - 40

2x^2 - 2x - 60 = 0

but then I'm stuck

... I think i know what to do once I get the values though
• May 12th 2009, 05:50 AM
mr fantastic
Quote:

Originally Posted by Calculusretard
guuh, I've been working on this problem forever and can't get it.

Find the area of the region bounded by the graphs f(x) = -x^2 + 7x + 20 and g(x) = x^2 + 5x - 40

To get the left and right x values

I do f(x) = g(x)

x^2 + 7x + 20 = x^2 + 5x - 40

2x^2 - 2x - 60 = 0

... I think i know what to do once I get the values though

Since you're studying calculus you're expected to be able to solve a quadratic equation. The x-coordinates of the intersection points are x = 6 and x = -5.

Draw a graph of the two curves and shade the required region. You should know that the enclosed area is given by $\int_{-5}^{6} \text{Upper curve} - \text{Lower curve} \, dx$.

It should be crystal clear from your graphs which is the upper curve and which is the lower curve. The integration is routine.
• May 12th 2009, 05:55 AM
Banned for attempted hacking
$2x^{2} -2x -60 =0$

$x^{2} -x -30 = 0$

$(x-6)(x+5)=0$

$x = -5 ,6$

Does that help ?
• May 12th 2009, 06:25 AM
Calculusretard
Ick. I got the wrong answer >_<

Thank you both for the responses!! Can either of you please tell me what I'm doing wrong/how to do it right!?

6
∫ -x^2 + 7x +20 - (x^2 +5x - 40) dx
-5

6
∫ -2x^2 + 2x + 60
-5

(-2x^3)/ 3 + (2x^2)/ 2

(-2(6)^3)/ 3 + (2(6)^2)/ 2 - ((-2(-5)^3)/ 3 + (2(-5)^2)/ 2)

And then I simplified it until I got 865/3 ... which is the wrong answer (Headbang)
• May 12th 2009, 08:10 AM
curvature
Quote:

Originally Posted by Calculusretard
Ick. I got the wrong answer >_<

Thank you both for the responses!! Can either of you please tell me what I'm doing wrong/how to do it right!?

6
∫ -x^2 + 7x +20 - (x^2 +5x - 40) dx
-5

6
∫ -2x^2 + 2x + 60
-5

(-2x^3)/ 3 + (2x^2)/ 2

(-2(6)^3)/ 3 + (2(6)^2)/ 2 - ((-2(-5)^3)/ 3 + (2(-5)^2)/ 2)

And then I simplified it until I got 865/3 ... which is the wrong answer (Headbang)

The graph of the region.