Question

5.) (8 pts.) Sketch the solid R in 3D-Space whose volume is given by the following double integral. (8 - 41 -2y) dy dz Jo Jo 6.) (10 pts.) Consider region R in 2D-Space, which is bounded by the y-axis and the right half of the circle given in polar coordinates by s = 4 sin 8. Find the I-coordinate of the Centroid of R (SET UP ONLY) using Rectangular Coordinates.

please answer 5 and 6

Answer 1

AS PER CHEGG POLICY, ONLY FIRST QUESTION IS TO BE ANSWERED. I HAVE SOLVED BOTH, BUT FULL EXPLANATION ARE NOT PROVIDED FOR SECOND. PLEASE DON'T MIND!

if we know that youme y region between . a plane region R t ag plane and a surface = Sa,) і яет н ) $4,9) 45 4х Herre faaliy) - 8-48-26 2=8-48-zy. > uatay +3=8 3 3 +4 +3 = -1), which is a blane having a intercept as a, y intercept as a and a intercept as 8. The region R is deteromined by o<H52, 027 54-23 - l from given It I limite is shown in figure. putting m=0 in ne get at al 7 22 tay =4 7 y =4nza which is same line as in R. org Thus, the region of integration Fig-i in given integraal is the volume in the octant bounded by plane in l). 22o y=4-22

It is shown in attached figure. —3+23- 6 is airen circle 7-45ho - -ца зр Теч) Э 4ч = ,50 X= [4, -у- за? 4 92 + -25-= 4 — 1) aaa luny 232 for right of x Thalf ă is the әхе Ачә- У clearly () is a circle with centra (92) and rading 2. w, я от Ajnok - ht< **viя к - Where R is the given s dyda region. х. У 494x 4cЧУур Х4-у-