   Chapter 5.4, Problem 50E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# The boundaries of the shaded region are the y-axis, the line y = 1, and the curve y = x 4 . Find the area of this region by writing x as a function of y and integrating with respect to y (as in Exercise 49). To determine

To find: The area of the shaded region.

Explanation

Given information:

The shaded region is bounded by a line with y=1 and a curve with y=x4.

The region lies between y=0 and y=1.

Express the curve function in terms of y:

y=x4 (1)

Rearrange Equation (1) to find the area of shaded region in terms of y.

x=y4

Find the area of the shaded region (A) as shown below:

A=abxdy (2)

Here, the curve function is x, the lower limit is a, and the upper limit is b.

Substitute y4 for x, 1 for b, and 0 for a in Equation (2)

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Study Guide for Stewart's Multivariable Calculus, 8th 