Show full and complete procedure HANDWRITTEN only. Please answer a) b) and c). Note they are subparts of the same question 1. Double Integrals in Polar Coordinatesa) Evaluate the integralR4 — x² - y²dA, where R = {(x, y)|x² + y² ≤ 4, x ≥ 0}b) Evaluate the integral [e-x²-y² dA, where R is the region bounded by the semicircle xеRR= 4- y² and the axis ŷ.c) Find the integral farctan(y/x) dA, where R = {(x,y)|1 ≤ x² + y² ≤ 9,0 ≤ y ≤ 2x}

Answered: Image /qna-images/answer/b2f9831b-34c7-438f-a3bb-d30db102dee0.jpg

L. Double Integrals in Polar Coordinates a) Evaluate the integral b) Evaluate the integral = R 4-x² - y²dA, where R = {(x, y)|x² + y² ≤ 4, x ≥ 0} e-x²-y² dA, where R is the region bounded by the semicircle x е R √4- y2 and the axis ŷ. c) Find the integral [ arctan (y/x) dA, where R = {(x, y)|1 ≤ x² + y² ≤ 9,0 ≤ y ≤ 2x} R

L. Double Integrals in Polar Coordinates a) Evaluate the integral b) Evaluate the integral = R 4-x² - y²dA, where R = {(x, y)|x² + y² ≤ 4, x ≥ 0} e-x²-y² dA, where R is the region bounded by the semicircle x е R √4- y2 and the axis ŷ. c) Find the integral [ arctan (y/x) dA, where R = {(x, y)|1 ≤ x² + y² ≤ 9,0 ≤ y ≤ 2x} R

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...

See similar textbooks

Similar questions

1) Evaluate the interated integral by converting to polar coordinates: V4-x2 A) LLVx? + y? dydx CHECK POINT B
Use polar coordinates to evaluate | 5x-y) dA where G is the region in the fourth quadrant bounded by the circles X+) x²+y²=1 x²+y²=4 Draw the region G. and
1) Evaluate the interated integral by converting to polar coordinates: CHECK POINT 2 V4-x2 B) SS sin(x2 + y?)dydx -2 0 Pal: A
2) Use polar coordinates to evaluate I| (2x + 3y) dA where R is the region in the first quadrant bounded by the circles x? + y? = 1 and x? + y? = 4 Also, sketch the region of integration in the xy-plane.
2-.Change the Cartesian integral into an equivalent Polar integral then evaluate the polar integral. You must sketch the area 4 V4x-x² 1 (x2 + y2)z dy dx 2 -V4x-x²
3) Evaluate the iterated integral by converting the to polar coordinates. -√₂x-x² a) So So √x²+y² dy dx a b) 56² 5 My dx (1+x² + y²) ³1² (930) () S 5 dy dx 4) Evaluate 2X a) S Socos (FX) dydx 1/2 2 -27 y³ b) So y xe dx dy П 25-x²
a) Sketch the region S enclosed by the curves y = Vx - 1 and y = (x – 1)². b) Find the Area of the region S.
4) Using Green's theorem, convert the line integral $(6y² dx + 2xdy) to a double integral, where C is the boundary of the square with vertices ±(2, 2) and ±(2, -2). ( do not evaluate the integral)
Sketch the region R in the first quadrant between the circles (x – })° + y² = } and (r -)? + y? = . 1 %3D |3D By first expressing I in terms of polar co-ordinates, evaluate I := Væ² + y² ° dx dy. R
3) Evaluate the double integral f,(x² + y²) dxdy using polar coordinates, where region Ris the semi-circle as given by shaded region in Figure. R (-2,0) (2,0)
Use Green’s Theorem to evaluate ∫ sin 5y dx + 5x dy around the boundary curve C of the region R, where R is the triangle formed by the point (0, 0), (1, 1) and (1, 3).
Use Green's Theorem to evaluate the line integral 6(e?cs* - 2y)dx+(5x+ ev dy, where C is the 2cosx 15. circle centered at the origin with radius 5.