Mass of one-dimensional objects Find the mass of the following thin bars with the given density function.?(x)= 1 + x3; for 0 ? x ? 1

Solution 10E Step1 Given that (x)= 1+x for 0x 1 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 Given (x)= 1+x on interval [0,1] The mass of bar in kilograms in b m= (x) dx a 1 3 = 1+x ] dx 0 x 1 =[x+ ] 4 0 Step5 m=(1+ )-(0+ ) 0 4 4 =1+ 4 5 = 4 Therefore, The mass of the thin bar using given density function is m= kg. 5 4