math question - calculus

Mathematics
Tutor: None Selected Time limit: 1 Day

A 3 centimeter piece of wire has density δ(x) = 1 + x 2 grams per centimeter at the point x centimeters from the left end. Where is the center of mass?

Jul 1st, 2015

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mass = the integral of (1+x^2)  = (x+x^3/3) &  evaluated at 0 and 3 = 3+9 = 12 gm

moment = the integral of x(1+x^2)  = (x^2/2 +x^4/4) &  evaluated at 0 and 3 = 4.5+20.25 =24.75 gm cm

therefore center of mass = moment/mass = 24.75/12 =2.0625 cm (Answer)

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Jul 1st, 2015

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