Areas between curves, Applications of Integrals

[alimarie333]

Hello,

I'm trying to solve a bunch of these word problems in my calculus class and cant figure out how to find the area.

1) Find the number "a" such that the line "x=a" bisects the area under the curve:

y=1/x^2 , 1 is less than or equal to x which is less than or equal to 4.

2) Find the number b such taht the line "y=b" bisects the area in the previous problem.

Thank you! This stuff is so hard!

 

[skeeter]

first, find the area under the curve 1/x² from x = 1 to x = 4 ...

\(\displaystyle \L A = \int_1^4 \frac{1}{x^2}dx\)

once you find the area, cut it in half ... A/2

then use the fundamental theorem of calculus to solve the following integral for "a" ...

\(\displaystyle \L \frac{A}{2} = \int_1^a \frac{1}{x^2}dx\)

the second problem is easy ...

using the area A that you found at the beginning, A/2 = 3b, solve for b.