Explanation Given: The provided integral is ∫ 0 2 ∫ x 2 2 x ( x 2 + 2 y ) d y d x . Formula used: Use the integration formula; ∫ x d x = x 2 2 Calculation: The function is firstly integrated with respect to y, taking x as a constant. Then, the limit of y is substituted. Again, the obtained function is integrated with respect to x . The integral is solved as follows: ∫ 0 2 ∫ x 2 2 x ( x 2 + 2 y ) d y d x = ∫ 0 2 [ x 2 y + 2 y 2 2 ] x 2 2 x d x = ∫ 0 2 [ ( x 2 ⋅ 2 x + ( 2 x ) 2 ) − ( x 2 ⋅ x 2 + ( x 2 ) 2 ) ] d x <

11th Edition

ISBN: 9781337275576

Author: Larson, Ron, Edwards, Bruce

Publisher: Cengage Learning,

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 14, Problem 4RE

To determine

To calculate: The value of the integral given as ∫02∫x22x(x2+2y)dydx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14, Problem 3RE

Chapter 14, Problem 5RE

Students have asked these similar questions

A helicopter pilot needs to travel to a regional airport 25 miles away. She flies at an actual heading of N16.26°E with an airspeed of 110 mph, and there is a wind blowing directly east at 20 mph. (a) Determine the compass heading that the pilot needs to reach her destination. (b) How long will it take her to reach her destination?

Question 3. the given integral is convergent or divergent: Use the comparison test to determine whether or not * sin*(x + 1) 7x3 (a) |. d.x g8 + x4 + 1 -dx (b) 2.x4 + x + 1

-d.x tan x

Chapter 14 Solutions

Calculus

Ch. 14.1 - CONCEPT CHECK Iterated Integral Explain what is...Ch. 14.1 - Prob. 2E Ch. 14.1 - Question: Evaluate the integral: 0x(2xy)dy Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an IntegralIn Exercises 310, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...Ch. 14.1 - Evaluating an Integral In Exercises 3-10, evaluate...

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 integral given as ∫ 0 2 ∫ x 2 2 x ( x 2 + 2 y ) d y d x .

Solution Summary: The author explains how the integral is solved by using the integration formula 8815.

Concept explainers

Videos

To calculate: The value of the integral given as ∫02∫x22x(x2+2y)dydx.

Want to see the full answer?

Chapter 14 Solutions