(i) Find the area of the region bounded by the curves x = y 5y+6 and...
2. (a) Find the area of the region bounded by the parabolas y 6z - 2 and y 22 (b) (Optional) Find the area of the region between the curves y2 and y - 22".. over the interval [0,2. 2 36 3. (Review) Evaluate the limit lim 4. (Review) A rectangle has its base on the z-axis and its two upper vertices on the curve y 5-x4. What is the largest area the rectangle can have? 2. (a) Find the...
Find the area of the region between curves 1. Find Find the area of the region between curves by rotating about x-axis the region in the x,y- plane bounded below and above, respectively, by the curves: a. y = 2x2, y = 4x + 16 b. x = -y2 + 10, x = (y – 2) I
(y=2 • A region is bounded by 3 functions: {x = y2 as shown. Clearly x=y construct a double integral to find its area using both dydx and dxdy orders. You do not need to evaluate the integral. 2
Find the area of the region bounded between the curves y = x and y = 2 – x2 by: a. Integrating with respect to x Integrating with respect to y
Q) Sketch the triangular region in the first quadrant bounded on the left by y-axis and the right by the curves:y-sinx and y-cosx, then find: 1)The area of the region? 2)The volume of the solid generated by revolving this region about the y-axis Q) Sketch the triangular region in the first quadrant bounded on the left by y-axis and the right by the curves:y-sinx and y-cosx, then find: 1)The area of the region? 2)The volume of the solid generated by...
6. (a) (1 marks) Sketch the region bounded by the curves y = sin x, y = x+1, x = 0 and x = - 27. (b) (3 marks) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line x = 27. (c) (3 marks) Use the method of washers to set up, but do not evaluate, an integral for the...
[4] Sketch the region bounded above the curve of y = x2 - 6, below y = x, and above y = -x. Then express the region's area as on iterated double integral ans evaluate the integral. -4 -3 -2 -1 0 1 2 3 4 [5] Find the area of the region bounded by the given curves x - 2y + 7 = 0 and y2 -6y - x = 0.
- -- - --10--- The region R is bounded by the curves y = 3.x, y = 9 - 22, and the y-axis, and its density is 8(x, y) = sy. To find the center of gravity of the pd (3) pdf92) pd 9() region you would compute 8(2,y)dA=1 62, y)dydx, 28(2,y)dydx, and 1 y(x,y)dyd. where Jc Jp(x) Je Jp(2) Jp(2) c= d= p(2) = 9(x) = pa pa(z) I dyda = Jo Ipa) 1 xdydx = I ydydx =...
Question 3: Find the area of the region bounded by the curves y = cos (x), y = 1 – cos (x), x = 0, and x = ſt.
Find the area of the region bounded by the two curves . y = x2 - 1, y = -x + 2, x = 0, x = 1 · y = -x + 3, y = x, x = -1, x = 1 . y = {x} + 2, y = x + 1, x = 0, x = 2