Question

3 Question 3 (2.5 points) We can express %** •/9r² ydydx = LS- r2 sin Odrdo in polar coordinates. Write a in the first blank, b in the second, c in the third and din the fourth blank. Write your answers in three decimal places. Calculate the integral and plug the answer in the fifth blank. Write your answer in three decimal places. Blank # 1 Blank # 2 Blank # 3 Blank #4 Blank # 5

Answer 1

3 5 ſa-x2 given, e 2 sino de do. y dy de O a С. for we x= r caso and the above transformation, put, y dx dy alisy de do 8(80) = ve sino Then, Now, alay) δι ar 2x де co seno ممهم- ay ay こ recos2ot le sinzo - O.1 = ve licos?00+ sin?0) ve dr do i dedy x² + y x=3 2 y = = 19-22 2 Also, = ve 2. it 18-0 From the is clear graph 2-3 that x=3 9-0 we varies from o varies from o to 3 o to L. And, Thosesforces y

9-22 3 y dy da ve sino si dr do 0 O 1 3 Ja-x2 3 y dy dx. se 2 sino de do Now, we will evaluate the above Integical ve ² sino de do 3 sino do. 3 O (3)3 sino do 3 n Х - cos 27 3 O [{cos - caso } 9 x [-(-1-1)] 94- (-2) } 9x2 18.

Blank #1 Blank # 2 Blank # 3 Blank # 4 3 Blank # 5 18 -