   Chapter 5.1, Problem 37E

Chapter
Section
Textbook Problem

# Use a graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately) the area of the region bounded by the curves. y = x   sin ( x 2 ) ,   y = x 4 ,   x ≥ 0

To determine

To find:

Approximate x-coordinates of the points of intersection of the given curves, and find the area of the region bounded by the curves.

Explanation

1) Concept:

Formula:

The area A of the region bounded by the curves y=f(x), y=g(x) and the lines x=a and x=b is

A= abfx-gxdx

fx-gx=fx-gx when fxg(x)gx-fx when gxf(x)

By substitution u=x2xsinx2= -12cosx2+c

2) Given:

y=xsinx2,   y=x4,  x0

3) Calculation:

fx=xsinx2,  and gx=x4

i) To find the intersection point of the curves, draw the graph

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