+ 7. (9 pts.) Given: f(x,y)=x-2y+3 and D is inside x² + y² = 16 and...
3. Evaluate the integral by changing to polar coordinates: SS (x+y) da R Where R is the region in quadrant 2 above the line y=-x and inside the circle x2 + y2 = 2.
3. Let D be the region in the first quadrant lying inside the disk x2 +y2 < 4 and under the line y-v 3 x. Consider the double integral I-( y) dA. a. Write I as an iterated integral in the order drdy. b. Write I as an iterated integral in the order dydx c. Write I as an iterated integral in polar coordinates. d. Evaluate I
Please do #2
40 1. 16 pts) Evaluate the integral( quadrant enclosed by the cirle x + y2-9 and the lines y - 0 and y (3x-)dA by changing to polar coordinates, where R is the region in the first 3x. Sketch the region. 2. [6 pts) Find the volume below the cone z = 3、x2 + y2 and above the disk r-3 cos θ. your first attempt you might get zero. Think about why and then tweak your integral....
Question 7 5 pts each Write iterated integrals for each of the given calu lations. Do not evaluate. (A) The integral of f(x, )212y over the domain D: 2 y 20. (B) The integral of f(x, y, z) = 12x + 3 over the volume contained in the first octant and below the graph z 8-y 2 (C) The mass of an object occupying the region bounded between the sur faces x2 + y2 + Z2 = 16 and z...
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 + z2 = 32. Consider (a) Write an iterated integral for the triple integral in rectangular coordinates. (b) Write an iterated integral for the triple integral in cylindrical coordinates. (c) Write an iterated integral for the triple integral in spherical coordinates. (d) Evaluate one of the above iterated integrals.
5. (2 points) Let S be the solid inside both x2+y2 = 16 and x2+y2 +...
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
10. Consider the integral (x + y + z) dV where D is the volume inside the sphere x2 + y2 + x2 = 9 and above the plane z = 1. (a) (3 marks) Express I as an iterated integral using Cartesian coordinates with the order of integration z, x and y. DO NOT EVALUATE THIS INTEGRAL. (b) (3 marks) Express I as an iterated integral using spherical coordinates with the order of integration p, 0, and 0. DO...
Can you please solve both of
these problems?
Evaluate the given integral by changing to polar coordinates. 9(x + y) dA where R is the region that lies to the left of the y-axis between the circles x2 + y2 = 1 and x2 + y2 = 4. , -378 Need Help? Read It Master It Talk to a Tutor -11 points v SCALCET8 15.3.511.XP. Evaluate the given integral by changing to polar coordinates. Il V25 – x2 + y2...
scan it clear please
7. (20points) Consider the following double integral: Hoc dA, where D is bounded by the upper semi circle y = V1 - 12 and the x-axis. (1) (Spoints) Find the Jacobian of the polar coordinates (2) (15 points) Evaluate the double integral by changing to polar coordinates.
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...