Chapter 5: Q. 3 (page 428)

State the integration-by-parts formula for indefinite integrals,
(a) using the notation $d u$ and $d v$ and
(b) without using the notation $d u$ and $d v$ .

Short Answer

Expert verified

The formula of integration by parts for indefinite integrals

Part (a) Using the notation $d u$ and $d v$ is localid="1649260912817" $\int u d v = u v - \int v d u$

Part (b) Without using the notation $d u$ and $d v$ is localid="1649261234065" $\int u (x) v^{ι} (x) d x = u (x) v (x) - \int v (x) u^{ι} (x) d x$

Step by step solution

Part (a) Step 1. Given information

We have to state the formula of integration by parts for the indefinite integrals using $d u$ and $d v$ .
Indefinite integrals are those integrals which do not have any upper limit and lower limit.

Part (a) Step 2. Formula with duand dv

The formula of integration by parts for indefinite integrals containing the notations $d u$ and $d v$ is $\int u d v = u v - \int v d u$

Part (b) Step 1. Given Information

We have to state the formula of integration by parts for the indefinite integrals using $d u$ and $d v$ .
Indefinite integrals are those integrals that do not have any upper limit and lower limit.

Part (b) Step 2. Formula with the notations du and dv

The formula of integration by parts for indefinite integrals not containing the notations $d u$ and $d v$ is, $\int u (x) v^{ι} (x) d x = u (x) v (x) - \int v (x) u^{ι} (x) d x$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

State the integration-by-parts formula for indefinite integrals,
(a) using the notation $d u$ and $d v$ and
(b) without using the notation $d u$ and $d v$ .

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Formula with duand dv

Part (b) Step 1. Given Information

Part (b) Step 2. Formula with the notations du and dv

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

State the integration-by-parts formula for indefinite integrals,(a) using the notation duand dvand(b) without using the notation duand dv.

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Formula with duand dv

Part (b) Step 1. Given Information

Part (b) Step 2. Formula with the notations du and dv

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Applied Mathematics

Probability and Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

State the integration-by-parts formula for indefinite integrals,
(a) using the notation $d u$ and $d v$ and
(b) without using the notation $d u$ and $d v$ .