1. The polar curves r@) = 1 + 2 sin(39), r = 2, are graphed below. 2 (a) Find the area inside the larger loops and outside the smaller loops of the graph of r 12 sin(30). [Hint: Use symmetry, the answer is 3v3.] [Answer: sf-i.] quadrant where r is maximum? (b) Find the area outside the circle r 2 but inside the curve r 1+2 sin(30) (c) What is the tangent line to the curve r-1+2sin(30) at the point...
14 only 13. Use double integrals to find the area inside the curve r = 1 +sin 14. (a) Express f Io ry dy dr as an integral over the triangle D, which is the set of (u. v) where 0s u s 1, 0 ssu (HINT: Find a one-to-one mapping T of D onto the glven region of integration.) (b) Evaluate this integral directly and as an integral over D* 15. Integrate ze+ over the cylinder 13. Use double...
Find the area of the region that lies inside the first curve and outside the second curve. r = 3 - 3 sin(θ), r = 3 Find the exact length of the curve. Use a graph to determine the parameter interval. r = cos2(θ/2)
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)
Problem #2/3 points total] 1. Graph 1lx2 -(22/2)x+Sy2 33 In your assignment submission, make sure that the scaling of both axes is the same (1 unit on the x-axis is the same length as 1 unit on the y axis) Insert the graph into your assignment submission. If necessary, scale the graph so that the scaling of both axes is the same Type or write, where you replace the italicized portion by your answer: The shape of the graph of...
1. Find the area (exact value) of the region that lies inside the curve r=5cosθ and outside the curve r=2+cosθ 2. Find the area (exact value) of the region that lies inside between curve r=5cosθ and r=2+cosθ 8. Find the area (exact value) of the region that lies inside the curve r = 5cose and outside the curve r = 2 + cose. 9. Find the area (exact value) of the region that lies inside both curves r = 5cose...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.) X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...
find the area of the graph formed by the given curve (3))2 a(! sin φ)(a) + 0). 9. Find the vnlume nf
please help! I cannot figure this out. The graph below is of the curve defined parametrically by: x-sin t and y- sin 2t -0 5 0.5 -1 (a) SET UP THE INTEGRAL TO FIND THE AREA OF THE REGION ENCLOSED BY THE CURVE AND EVALUATE (b) SET UP THE INTEGRAL TO FIND THE LENGTH OF THE CURVE TRAVERSED EXACTLY ONCE. DO NOT EVALUATE. SIMPLIFY TO JUST BEFORE MAKING A SUBSTITUION. (c) SET UP THE INTEGRAL TO FIND THE TOTAL DISTANCE...
Consider the polar graph r=1-sin theta and r= sin theta, shown below. Please help with B, D, and E 5. Consider the polar graphs r = 1-sin 0 and r = sin 0, shown below. a. Find the polar coordinates (r, 2) for all points of intersection on the figure. Hint: Not all points can be found algebraically. For b.-d., set up an integral that represents the area of the indicated region. b. The region inside of the circle, but...