П Find the length of the curve y = In (2 sec x) from 0≤x≤6 Set up the integral that gives the length of the curve. Use increasing limits of integration. JOdx dx (Type exact answers.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question
П
Find the length of the curve y = In (2 sec x) from 0≤x≤6
Set up the integral that gives the length of the curve. Use increasing limits of integration.
JOdx
dx
(Type exact answers.)
Transcribed Image Text:П Find the length of the curve y = In (2 sec x) from 0≤x≤6 Set up the integral that gives the length of the curve. Use increasing limits of integration. JOdx dx (Type exact answers.)
Find the volume of the solid generated when the region bounded by the graph of y = sin x and the x-axis on the interval [1, 2] is revolved about the x-axis.
The described volume is cubic units.
(Type an exact answer, using it as needed.)
Transcribed Image Text:Find the volume of the solid generated when the region bounded by the graph of y = sin x and the x-axis on the interval [1, 2] is revolved about the x-axis. The described volume is cubic units. (Type an exact answer, using it as needed.)
Expert Solution
Step 1: Introduction

Solution:

Given, y=ln(2 sec x) from 0xπ6

 

The formula for the length of the curve y=f(x) in axb is

 L =ab1+dydx2dx   ,    b is the upper limit, is the lower limit.

Formula: absec(x)dx=lnsecx+tanxab

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