Question

12

10. Find the area enclosed by the polar curve 2 11 cos (80). 11T Hide Elapsed: 0000 27 Instructions O22π 11. This question is worth 20 points. You must complete both parts. Parts (a) and (b) are not related and should be answered as separate, distinct problems. θ2,0 θ (a) (10 points) Graph the polar curve r (b) (10 points) Find the surface area given by rotating the curve ya froma1 to 3 about the z axis. 12. This question is worth 20 points. You must complete both parts. Parts (a) and (b) are not related and should be answered as separate, distinct problems. (a) (10 points) Find the area between the r axis and the curve given by the parametric functions 3 cost cos 3t y-3 sin t-sin 3t from t 0 to t-T. (b) (10 points) Find the length of the curve y2 14) from 0 to 2, where y > 0.

Answer 1

answer 10 is -11

explanation

r^2= a^2+b^2

a=r sin A

b=r cos A

A is the angle between the a &b.

area of curve is given by =1/2(a*b)

hint ;

2 sin(x)cos(y)=​ [sin(x+y)+sin(x−y)