1. How do you find the area of a region bounded by a polar curve? 2....
3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
Use a double integral in polar coordinates to find the area of the region bounded on the inside by the circle of radius 5 and on the outside by the cardioid r=5(1+cos(θ))r=5(1+cos(θ))
4. Consider the area of the region that lies inside the curve given in polar form) by r = 6 sin(@) and outside the cardioid given by r=2+2 sin(0). (a) (3pts) Set up but do not evaluate an integral(s) which represents the area of this region. (b) (3.5pts) Evaluate this integral to determine the exact area of this region. (Hint: you will need to use a trig, identity)
c. Sketch the curve and find the area of the region that lies outside r 2sin0 and inside r=sin0+cos (you must use integral for this question, otherwise(like using formula for area of a circle, etc.,) you will get 0 point) c. Sketch the curve and find the area of the region that lies outside r 2sin0 and inside r=sin0+cos (you must use integral for this question, otherwise(like using formula for area of a circle, etc.,) you will get 0 point)
Question 1 (1 point) Find the length of the spiraling polar curve r = 3e60 From 0 to 21 . The length is (1 point) Find the area of the region that is bounded by the curve r = V6 sin(0) and lies in the sector 0 Sost. Area =
Find the area of the region that is bounded by r = sin 0 + cos 0, with 0 <OST. Find the area of the right half of the cardioid: r = 1 + 3 sin .
1-Cos(24) as O t 7, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(r, y) ()) m, which I have drawn for you below. Find the area bounded by this curve and the X-axis. (Hint: Use Green's Theorem with F(x,)-().) (6) Consider the curve expressed by the polar equation T-0, as 0 1-Cos(24) as O t 7, which I have drawn for you below. Find the...
Find the area of the region bounded by the curves r = 2 + cos(2), 0 = 0, and = /4. You may need the formulas: cos” (a) = 1+ cos(22), sin?(x) = 1 – cos(22)
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
Solve 1A & 1B 1A) Find the area of the region that is bounded by the given curve and lies in the specified sector. r = θ2, 0 ≤ θ ≤ π/6 1B) Find the area that r = 1 + sin(4θ) encloses.