Problem

Calculate the average value of $ f(x) = x \sec^2 …

03:46

Problem 65 Hard Difficulty

Calculate the volume generated by rotating the region bounded by the curves $ y = \ln x $, $ y = 0 $ and $ x = 2 $ about each axis.
(a) The y-axis
(b) The x-axis

Answer

a) $\pi\left(4 \ln 2-\frac{3}{2}\right)$
b) $\pi\left[2(\ln 2)^{2}-4 \ln 2+2\right]=2 \pi\left[(\ln 2)^{2}-2 \ln 2+1\right]$

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

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Video Transcript

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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 7

Techniques of Integration

Section 1

Integration by Parts

Problem

Calculate the average value of $ f(x) = x \sec^2 …

Problem 65 Hard Difficulty

Calculate the volume generated by rotating the region bounded by the curves $ y = \ln x $, $ y = 0 $ and $ x = 2 $ about each axis.
(a) The y-axis
(b) The x-axis

Answer

a) $\pi\left(4 \ln 2-\frac{3}{2}\right)$
b) $\pi\left[2(\ln 2)^{2}-4 \ln 2+2\right]=2 \pi\left[(\ln 2)^{2}-2 \ln 2+1\right]$

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 2 / BC Educators

Anna Marie V.

Kayleah T.

Kristen K.

Joseph L.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

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Watch More Solved Questions in Chapter 7

Video Transcript

Calculus: Early Transcendentals

Grace H.

Catherine R.

Caleb E.

Michael J.

Integration Review - Intro

Definite vs Indefinite

a) $\pi\left(4 \ln 2-\frac{3}{2}\right)$b) $\pi\left[2(\ln 2)^{2}-4 \ln 2+2\right]=2 \pi\left[(\ln 2)^{2}-2 \ln 2+1\right]$

Calculus: Early Transcendentals

Anna Marie V.

Kayleah T.

Kristen K.

Joseph L.

Integration Review - Intro

Definite vs Indefinite

Grace H.

Catherine R.

Caleb E.

Michael J.

a) $\pi\left(4 \ln 2-\frac{3}{2}\right)$
b) $\pi\left[2(\ln 2)^{2}-4 \ln 2+2\right]=2 \pi\left[(\ln 2)^{2}-2 \ln 2+1\right]$