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.
Find the area of the region in the XY-plane enclosed by y = 3−x and x...
3. Find the total area of the region enclosed by the curve y=xsin x and the x-axis from (0,37). The graph is shown below. Show all of your work! (Hint: You will need multiple integrals here)! (8 pts)
Find the volume generated by revolving about the x-axis, the region enclosed by y=x^2+1 and 3x−2y=−4 Be sure to draw the region in the x-y plane, label the axis of revolution, state your method (disc or shell), draw a rectangle to be rotated, label the thickness (dx or dy), state the integral, and sketch the resulting 3D shape. State the volume exactly. show all work please.
Sketch the region enclosed by the curves y = x + 2, y = 16 – x2 , x = – 2, and x = 2 on your paper. Find the area of the region. Show all steps mathematically connected.
Find the area enclosed by the parabola y2-3y+4 and the line x 2y+4 ts where the parabola and the line intersect. Give your answer as a comma-separated list of points, e g Worksheet b) Determine the area of the enclosed region. Give your answer as an exact expression Worksheet Area 100%
Find the area enclosed by the parabola y2-3y+4 and the line x 2y+4 ts where the parabola and the line intersect. Give your answer as a comma-separated list of...
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the xy- plane bounded by y x,y 0 and x.(b) Let f(x)-2 (n+3)2 _____ for each x for which the series o 5" converges. Write a power series in summation notation for an indefinite integral of f.
10. (a) Find the surface area of the portion of the graph of f(x, y)-yx which is above the region in the...
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
xy=1 and y 2x V -X -Region S is bounded by the lines xy 2. Draw the region and indicate all the vertices. and the hyperbolas 2 and B) Transfer region S from x-y to u-v plane and indicate all the vertices on the new plane acx. y au,v) =1 C) Show that the area corrections are related by (u,v) x, y) D) Find the centroid of region S
xy=1 and y 2x V -X -Region S is bounded by...
Find the area of the region enclosed by y = (x + 2)^2, y = 1/x + 2 , x = − 3/2 and x = 1.
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)...
The area of the region enclosed by the curves y = 2x, 3y = X and 2y = -x+5 is none of these o o 3,5 0 2.5 0 o o