11. Use the graph of two curves below to find the following: a. Find the y-values...
find the area of the region bounded by the graphs of the two equations below. How do you know where they intersect? How do you find the values of a and b? How do you know which is the upper graph and which is the lower graph? please explain how you got it thanks. THEOREM6 Let f and g be continuous functions with (x) 2 g(x) over [a, b]. Then the area of the region between the two curves, from...
1 The following questions involve the two polar curves: Sketch the curves and shade the region outside R and inside r Use a large size graph paper a l clearly indicate the points of intersection. Also indicate the values of theta that give one complete cycle for each curve b. Discuss the symmetry of each curve c. Calculate th e area for the region of overlap that you shaded and described in part a. Show all steps clearly and neatly....
5. (10 pts.) Find the area shaded below which is bounded by the curves y = x2 (red), y = x + 2 (blue) and x axis. (The graph is not drawn to scale). y=x2 y=x+2
In the picture below is a shade region between the curves y= -2r + 1 and y = 2 - 2 for-1 Srs 1. Set up, but do NOT evaluate, a definite integral that can be used to find the area of the shaded region.
[11 Marks) ii) Determine the shaded area enclosed between the given two curves 3 +2, y = x + 2 4 y =
2. Graph the following equations and shade the area of the region between two curves. Determine its area by integrating over x-axis or y-axis, whichever seems convenient. y = v* and 2y + x 3 = 0.
Find the centroid (center of mass) of the region between the curves y = x and y = x4. (Note:these curves intersect at the origin and at the point (1,1).)
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately- three decimal places) the area of the region bounded by the curves. Also, make a rough sketch of the region sought. You must write the definite integral using proper notation to receive full credit 1) y = χ sin(x*) , y = x6 Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves....
5. The graphs of the polar curves r-4 and r-3 + 2 cos θ are shown in the figure above. The curves intersect 3 (a) Let R be the shaded region that is inside the graph of r-4 and also outside the graph of r 34 2 cos θ, as shown in the figure above. Write an expression involving an integral for the area of R. (b) Find the slope of the line tangent to the graph of r :-3...
1. The following questions involve the two polar curves: R 2+2sin20 and r 6sin 0 Sketch the curves and shade the region outside R and inside r. Use a large size graph paper and clearly indicate the points of intersection. Also indicate the values of theta that eive complete cycle for each curve. a b. Discuss the symmetry of each curve. ulate the area for the region of overlap that you shaded and described in part a. Show all steps...