Question: QUESTION 2 (20 MARKS) (a) Evaluate the integral (2x + y?) dx dy. by first converting it into an integral in polar coordinates. (7 marks)

QUESTION 2 (20 MARKS) (a) Evaluate the integral (2x + y?) dx dy. by first converting it into an integral in polar coordinates. (7 marks) (b) Find the mass of the solid in the first octant bounded by the planes y = 0, z = 0 and y = x, and z = 4 - x2 with density 6(x, y, z) = Ty. (6 marks) (c) Evaluate the integral . 1-x2-ya 22 dz dr dy. (15.1) I? + y2 + 22 by first converting it to an integral in spherical coordinates. (7 marks)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Question 1 1 pts Evaluate the integral. 9- x2 x dy dx O 27 O 81 4 O 27 0 9 Question 2 1 pts Integrate the function f over the given region. f(x, y) = y2 ex over the triangular region in the first...

5. [-/1 Points] DETAILS SCALC8 15.3.020. Use polar coordinates to find the volume of the given solid. Below the cone z = v x2 + y2 and above the ring 1 s x2 + y2 s 25 Submit Answer 6. [-/1 Points]...

1. Use double integration in polar coordinates to find the volume of the solid that lies below the surface z = 5 + x y and above the circle x 2 + y 2 = x in the xy-plane. 2. Find the area of the...

SECTION A Instructions: On the inside cover of the examination answer booklet provided, shade the letter that corresponds with the most appropriate response for each of the following. 1. What is the...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Sun Inc. manufactures hydrogen engines. Recently 350 new orders placed by customers requesting credit. The variable cost is $16,000 per unit, and the credit price is $18,400 each. Credit is extended...

MA 261 PRACTICE PROBLEMS 1. If the line ` has symmetric equations y x1 z+2 2 = 3 = 7 , nd a vector equation for the line `0 that contains the point (2; 1; 3) and is parallel to `. A. ~ = (1 + 2t)~...

sjeccd.instructure.com 15 Group Quiz C Find The Average Value Of The Following Regions F(.. | Chegg.com Question 11 0.5 pt Find the area of the region specified in polar coordinates. the region...

Question 2: Explain geometrically how the formula for a single A is obtained. Explain why this area depends on r and not just r. Note that this is about just a single "polar rectangle" and not the...

5. [-/0.385 Points] DETAILS LARCALC11 14.2.013. Set up integrals for both orders of integration. Use the more convenient order to evaluate the integral over the plane region R. xy dA R: rectangle...

Why are environmental scanning and analysis important to marketers?

Right/Responsibilities, result, reputation, relationship lens. Each of the ethical lenses has both vices (deliberate actions making an unethical choice) and risks (unexpected consequences). These...

Which of the following is part of the ETL process? Tuning the data warehouse database to make it run efficiently. Transforming the data so inconsistent, inaccurate, or missing data is converted...

A hula hoop and solid disc of equal radii are rolled, from rest and without slipping, down an incline plane. Which one will reach the bottom of the inclined plane first? Explain.

Charlie wants to start a small machine shop. He plans to place all welding equipment in one area, all grinding and milling equipment in another area, and all drilling equipment in another area. What...

Which of the following was not cited as an advantage of working in a home office? a. flexibility in scheduling b. low overhead expenses c. no commute time d. no interruptions

T F Neither agents nor brokers take title to goods.