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Calculus/Area of a region.

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Expert: - 1/13/2011


Question
Hi. My question is:

Sketch the region between y = ln(x-1), y=1, y=0 and x- y^4 +1=0
and find the area of this region.

I think I have sketched it out correctly but can you help me find the area?

Answer

Graph
Hello Talha,

I have attached an image of the sketch.

We take horizintal "slices" so dA=([x-value on y=ln(x-1)]-[x-value on x-y^4+1=0]) dy
Thus, dA=([1+e^y]-[y^4)-1) dy...now integrate from y=0 to y=1
A=[y+e^y-y^5/5+y] from y=0 to y=1
= e + 4/5

OK?

Abe

Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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