Explanation Solve the integral ∫ x x 2 + 2 3 d x by substitution method. Let u = x 2 + 2 then d u is, d u d x = d ( x 2 + 2 ) d x = d ( x 2 ) d x + d ( 2 ) d x = 2 x + 0 d u = 2 x d x Rewrite the original integral in terms of u as follows. ∫ x x 2 + 2 3 d x = 1 2 ∫ u 3 d u = 1 2 ∫ u 1 3 d u = 1 2 ( 3 4 u 4 3 ) + C = 3 8 u 4 3 + C Substitute the value of u = x 2 + 2 in the above solution, the value of the given integral is 3 8 ( x 2 + 2 ) 4 3 + C

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 8.1, Problem 22E

To determine

To find: The value of the definite integral ∫05xx2+23dx .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.1, Problem 21E

Chapter 8.1, Problem 23E

Students have asked these similar questions

Use the shell method to find the volume of the solid generated by revolving the region bounded by the curves and lines about the y-axis. y=x², y=7-6x, x = 0, for x≥0

The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = −3. -7-6- -5- +1 23456 1 2 3 4 5 67 Select the correct answer below: ○ f(x) is not continuous at x = f(x) is not continuous at x = f(x) is not continuous at x = f(x) is continuous at x = -3 -3 because f(-3) is not defined. -3 because lim f(x) does not exist. 2-3 -3 because lim f(x) = f(−3). 2-3

Could you explain how this was solved, I don’t understand the explanation before the use of the shift property As well as the simplification afterwards

Chapter 8 Solutions

Calculus with Applications (11th Edition)

Ch. 8.1 - YOUR TURN 1 Find Ch. 8.1 - YOUR TURN 2 Find Ch. 8.1 - YOUR TURN 3 Find Ch. 8.1 - YOUR TURN 4 Find . Ch. 8.1 - YOUR TURN 5 Find Ch. 8.1 - Prob. 1WE Ch. 8.1 - Find the following. W2. Ch. 8.1 - Find the following. W3. Ch. 8.1 - Find the following. W4. Ch. 8.1 - Use integration by parts to find the integrals in...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The value of the definite integral ∫ 0 5 x x 2 + 2 3 d x .

Concept explainers

Videos

To find: The value of the definite integral ∫05xx2+23dx .

Want to see the full answer?

Chapter 8 Solutions