Q6P 鈭珁-12鈭玿-yy2xdxdy... [FREE SOLUTION]

Chapter 5: Q6P (page 247)

${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} x d x d y$

Short Answer

Expert verified

The required solution is ${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} xdxdy \frac{47}{20}$ .

Step by step solution

Definition of Definite Integral

The antiderivative and indefinite integrals of a function are closely connected to the definite integral. The indefinite integral, if it exists, has a real numerical value, whereas the latter two represent an unlimited number of functions that differ only by a constant.

Finding the Integral

Consider the given integral,

${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} xdxdy = {鈭�}_{y - 1}^{2} [\frac{1}{2} x^{2}_{\sqrt{y}}^{y^{2}}] d y = \frac{1}{2} {鈭�}_{1}^{2} (y^{4} - y) d y = \frac{1}{10} y^{5}_{1}^{2} - \frac{1}{4} y^{2}_{1}^{2} = \frac{1}{10} (32 - 1) - \frac{1}{4} (4 - 1) = \frac{62}{10} - \frac{15}{20} = \frac{47}{20}$

Therefore, the solution is ${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} xdxdy = \frac{47}{20}$ .

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} x d x d y$

Short Answer

Step by step solution

Definition of Definite Integral

Finding the Integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Quantum Physics

Measurements

Fluids

Kinematics Physics

Dynamics

Study anywhere. Anytime. Across all devices.

91影视

鈭�y-12鈭�x-yy2xdxdy

Short Answer

Step by step solution

Definition of Definite Integral

Finding the Integral

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism and Electromagnetic Induction

Quantum Physics

Measurements

Fluids

Kinematics Physics

Dynamics

Study anywhere. Anytime. Across all devices.

${鈭�}_{y - 1}^{2} {鈭�}_{x - \sqrt{y}}^{y^{2}} x d x d y$