Sunday

September 21, 2014

September 21, 2014

Posted by **Francesca** on Thursday, June 14, 2012 at 12:10pm.

f(x) = 36 - x^2; [-1,13]

So, what does be the area between the x-axis and f(x) equal? Thank you for any help! I'm really confused with this problem!

- Math -
**Steve**, Thursday, June 14, 2012 at 12:58pmDo you mean algebraic (signed) area? If so, that is -686/3.

If you mean actual physical area, where area below the axis is also considered positive, then you have to break the area into the part above the axis [-1:6] and below the axis [6:13]. Doing it that way, we get 588.

- Math -
**Francesca**, Thursday, June 14, 2012 at 1:14pm588 is the correct answer? But, I don't understand how to get to that number. How did you calculate that? Sorry, that may be a lot to type out

- Math -
**Francesca**, Thursday, June 14, 2012 at 1:14pm588 is the correct answer!**

- Math -
**Steve**, Thursday, June 14, 2012 at 5:39pmThe graph crosses the x-axis at (6,0)

integrate 36-x^2 from -1:6 to get the positive area

integrate -(36-x^2) from 6:13 to add the area below the axis instead of subtracting it

∫[-1,6](36-x^2) + ∫[6,13](x^2-36)

= (36x - x^3/3)[-1:6] + (x^3/3 - 36x)[6,13]

539/3 + 1225/3 = 1764/3 = 588

**Answer this Question**

**Related Questions**

Calculus - Use the limit process to find the area of the region between the ...

Calculus - These are the two problems from my homework I don't get.. can you ...

math - Consider the area between the curve y=x^2 and the x-axis over the ...

calculus - Find the area between the graph of f and the x-axis over the interval...

Calculus - Can someone look over my work and tell me if my steps look correct? I...

Calculus - Would someone clarify this for me... Is antiderivatives just another ...

calculus(Lab) - Well, first graph the graph of f(x)=-1/10x^2 + 3 2. We are going...

Math - a) Is ∫[-1 to 1]e^x^3 dx positive, negative, or zero? Explain. I think ...

Fundamental Theorm of Calculus - Use a definite integral to find area of the ...

Math - Use the limit process to find the area of the region between f (x)=10x+8 ...