Problem 9E

Mass of one-dimensional objects Find the mass of the following thin bars with the given density function.

ρ(x) = 1 + sin x;for 0 ≤ x ≤ π

Solution 9E Step1 Given that (x)= 1+sin x for 0x Step2 To find Mass of the thin bar using given density function. Step3 Mass of the object is b m= x) dx a Let a thin bar can be represented as a line segment on the interval axb with a density function, (with units of mass per length). Step4 The mass of bar in kilograms in b m= x) dx a = [1+sinx] dx 0 =[xcos x] 0 Step5 m=(- cos )-(0-cos 0) =( -(-1))-(-1) =+2 Therefore, The mass of the thin bar using given density function is m=+2 kg.