   Chapter 8.5, Problem 55E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Finding the Area of a Region In Exercises 53-56, sketch the region bounded by the graphs of the functions and find the area of the region. y = 2 sin   x ,   y   = tan x ,   x = 0 ,   x = π 3

To determine

To graph: The region bounded by the functions, y=2sinx and y=tanx for x=0 to x=π3 and also calculate the area of the region.

Explanation

Given Information:

The provided functions are y=2sinx and y=tanx for x=0 to x=π3.

Formula used:

Write the formula of definite integral of abtanudu.

abtanudu=[ln|cosu|]ab

Write the formula of definite integral of absinudu.

absinudu=[cosu]ab

Graph:

Draw area bounded by graph of y=2sinx and y=tanx for x=0 to x=π3.

Consider provided function.

y=2sinx

At x=0,

yx=0=2sin(0)=0

At x=π6,

yx=π6=2sin(π6)=2(0.50)=1

At x=π6,

yx=π3=2sin(π3)=2(0.866)=1.732

Now, the table for ordered pair (x,y) for the function y=2sinx is shown below,

xy00π61π31.732

Again, consider provided function,

y=tanx

At x=0,

yx=0=tan(0)=0

At x=π6,

yx=π6=tan(π6)=0.577

At x=π3,

yx=π3=tan(π3)=1.732

Now, the table for ordered pair (x,y) for the function y=tanx is shown below,

xy=tanx00π60.577π31.732

Thus, the resulting graph of y=2sinx and y=tanx for x=0 to x=π3 is,

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 