3. Find the total area of the region enclosed by the curve y=xsin x and the...
Find the area of the region in the XY-plane enclosed by y = 3−x and x = 3y−y . In doing so, sketch the region (hint: remember that the graph of a quadratic is a parabola), and be sure to show all your work.
2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following definite integrals: (a) cos(x) da (sin(x) +18 (b) COS 4. The graph of y=g(t) is shown below, and consists of semicircles and line segments. y=g() -1 3 6 596 s(t) dt Define the function f(x) by f(x)= Use the graph of y = g(t) and the properties of the definite integral to find: (a) the value of (i) f(3) (ii) f(-1) (iii) 1'(6) (b)...
t2-2t, y =vt and the y-axis. Find the area enclosed by the curve x t2-2t, y =vt and the y-axis. Find the area enclosed by the curve x
please add graph if any (b @ Find the area of the region enclosed by y=x andy= 5x3². up the Intergral representing the volume of the solid obtained by rotating about the masis the region bounded by y=2+1 and y=3-x² about the x-axis set
lamina with density ρ(x,y) = 3 √{x2+y2} occupies region D, enclosed by the curve r = 1−sin(θ). Which of the following statements is the best description of the center of mass of the lamina? Find the moments of intertia about the x-axis, the y-axis, and the origin for the lamina. Yes, the integrals can be done by hand, but why put yourself through that? You may round your answers to the nearest 0.01.
The region enclosed by the curve y=8sechx, the x-axis, and the lines x=±ln3 is revolved about the x-axis to generate a solid. Find the volume of the solid. The region enclosed by the curve y = 8 sechx, the x-axis, and the lines x= + In 13 is revolved about the x-axis to generate a solid. Find the volume of the solid. Setup the integral for the volume. V= Type an exact answer, using n as needed.) The volume is...
Find the total area of the region between the curve and the x-axis. y = x2 - 6x + 9; 2 sx54
17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work) 17) Let Rbe the region enclosed by the loop in the curve x-t, y--t34t.If Ris rotated about the x-axis, find the volume of the resulting solid parametrically. (Show your work)
16 pts) 1. Determine the area of the region between the two curves y=x and y+2x by integrating over the x-axis. Hint: Refer the figure and note that you will have two integrals to solve by splitting the region between the two curves into two smaller regions. lo pl [6 pts) 2. Find the area of the region bounded by the curves y=12 - x, y=vx, and y20
Home Work Task 1 Total M Determine the area of the region enclosed by the two curves y = sin2x and y = cosx by sketching the curves in (-1,1]. Find the area enclosed by, 1x + y - 11 + 12x + y - 11 = 1 By sketching the graph. 3 Sketch the graphs for the parabolas whose equations are, y = -x2 + 5x + 9 and y = x² + 3x + 5 Find the area...