(i) Find the area of the region bounded by the curves x = y
5y+6 and x =-y +y+6
Q.2 A. (1) Find the area of the region bounded by the curves x = y2 - 5y +6 and x=-y+y+6 (2 Marks) In(tan x) (ii) Evaluate lim (3 Marks) sinx-cosx B. (1) Evaluate |fxsin(xy dydx (3 Marks) X- (1) Evaluate lim * (11) Evaluate tan lim- (2 Marks) 2 Marks) - tan
2 10. Find the area of the region bounded by the curves y= V5 – x and y = Vä
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
Sketch the region bounded by the curves y=e^x ,y=-x+2 and x=0, generate an integral of type-I and type-II, representing the volume of the enclosed region.
Question 3: Find the area of the region bounded by the curves y = cos (x), y = 1 – cos (x), x = 0, and x = ſt.
(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
For the lamina that occupies the region D bounded by the curves x = y2 – 2 and x = 2y + 6, and has a density function: p(x, y) = y + 4, find: a) the mass of the lamina; b) the moments of the lamina about x-axis and y-axis; c) the coordinates of the center of mass of the lamina.
5. Find the volume of the solid obtained by rotating the region bounded by the curves, y = 2x, x = 0 and y = 10 about the x axis,
5. Find the volume of the solid obtained by rotating the region bounded by the curves, y = 2x, x = 0 and y = 10 about the x axis,
the solid obtained by revolving the region bounded by the curves x= sqr root y and x=-y^2 when x=-3. find the volume.
The region Bounded by the
curves y=x2 is revolved about the x-axis. Give an
integral for the volume of the solid that is generated.
The region bounded by the curves y = 3x and y = x' is revolved about the x-axis. Give an integral for the volume of the solid that is generated. va | ndx (Type an exact answer using a as needed.)