Area between curves Let R be the region bounded by the graphs of y = e−ax and y =e−bxfor x ≥ 0, where a > b > 0. Find the area of R.
Area between curves Let R be the region bounded by the graphs of y = and y =for x ≥ 0, where a > b > 0. Find the area of R.
Let R be the region bounded by the graph of y = and y =for x ≥ 0, where a > b > 0.
Now , we have to find out the area between the curves.
Given a > b > 0, in the interval [0, infinity), the graph of e−bx will always be above the graph of e−ax. So the setup of the area integral is ∫(e−bx − e−ax)dx from 0 to ∞. This can be rewritten as the difference of two integrals:
Put -bx = t , then -b dx = dt
dx = dt
Therefore, = (dt)
Textbook: Calculus: Early Transcendentals
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. Since the solution to 57E from 7.7 chapter was answered, more than 315 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 57E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This full solution covers the following key subjects: area, Find, bxfor, curves, bounded. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The answer to “Area between curves Let R be the region bounded by the graphs of y = e?ax and y =e?bxfor x ? 0, where a > b > 0. Find the area of R.” is broken down into a number of easy to follow steps, and 33 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1.