A slender metal rod of length 30 centimeters lies along the –axis with its left end…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A slender metal rod of length 30 centimeters lies along the x–axis with its left end at the origin. The rod’s linear mass density, in grams per centimeter, is given by the exponential model λ(x)=5e−0.10x for 0≤x≤30.
(a) Set up, but do not evaluate, a definite integral whose value gives the total mass of the rod.
(b) Evaluate the integral from part (a) to the nearest tenth of a gram.
(c) Verify that the integrand you used in part (a) has units of grams per centimeter and that the result of the integral has units of grams.