Mass of one-dimensional objects Find the mass of the following thin bars with the given density function.? (x) = 5e?2x: for 0 ? x ?4

Solution 12E Step1 Given that (x)= 5e 2xfor 0x4 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 2x Given (x)= 5e on interval [0,4] The mass of bar in kilograms in b m= x) dx a 4 = 5e 2x] dx 0 4 2x =5 e ] dx 0 e2x4 =5[ 2] 0 Step5 m= 25[e 2*4-e2*0] 5 8 0 = 2 [e -e ] = 5[e -1] 2 5 = 21e ] 8 Therefore, The mass of the thin bar using given density function is m= [1e2] 8 kg.