   Chapter 7.2, Problem 58E

Chapter
Section
Textbook Problem

# Find the area of the region bounded by the given curves. y = tan x ,     y = tan 2 x ,    0 ≤ x ≤ π / 4

To determine

To evaluate: area of the region bounded by two given curves

Explanation

Consider a function y=f(x) between the points x=a and x=b. The area under this graph between the two points is given by the following integral:

A=abydx

Then, the area between two curves will be given by the difference between the area under their respective graphs.

Formula used:

Area between two curves f and g is given by:

A=ab|(f(x)g(x))|dx

Given:

The two curves, y=tanx,y=tan2x.

The limit 0xπ4

Calculation:

Substitute the curves into the formula to get;

A=0π4|(tanxtan2x)|dx=0π4tanxdx0π4tan2xdx           (tanxtan2x for 0

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