5. (10 pts.) Find the area shaded below which is bounded by the curves y =...
3. (10 pts) Find the area of the region bounded between y = xe-*?, , y = x + 1, x = 2 and the y-axis. Note that the graph of the region is provided below. You can leave your answer in terms of e. y=x+1 x2 X-0 0 0.5 1. 0 dy Use the Fundamental Theorem of Calculus to find dx for y = = L* sin (t2)dt.
show all work 1. Find the area of the region bounded by the curves below. Sketch a graph of the region first. a. x = y2, x = VD, y = 0 b. y = x2 – 4, y == x2 + 4
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
Find the area of the shaded region bounded by y = 2x and y = xV49 – x2 in the figure. 2. (Give an exact answer. Use symbolic notation and fractions where needed.)
The shaded area shown below is bounded by the line x - 9m on the left, the x-axis on top, and the curve y - (-18x + x2) m on the right. 9 m 18 m y=(-18x+x®) m -81 m Determine the coordinates of the centroid of the area in meters. m y = m Determine the coordinates of the centroid of the shaded area in millimeters. y 4 mm y = (0.9x* - 57.6 x) mm mm XI mm
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
The shaded area shown below is bounded by the line x = 9 m on the left, the x-axis on top, and the curve y = (-18x + x2) m on the right. 9 m 18 m y=(-18 x + x) m -81 m Determine the coordinates of the centroid of the area in meters. m IX I m
Problem 3 (20 points) - The shaded area shown below is bounded on the right at x 2 ft, bounded on the top by the equation y-(%), and bounded on the botton by the equation y x. The shaded area has a magnitude of A-4 Using the integration method, determine the vertical location of the centroid () with respect to the x-axis shown. SOLUTIONS y (ft) -2
2 10. Find the area of the region bounded by the curves y= V5 – x and y = Vä
B Consider the shaded region bounded by y=x2 – 4 and y= 3x + 6 (see above). Note that the r-axis and y-axis are not drawn to the same scale. (a) Find the coordinates of the points A, B, and C. Remember to show all work. (b) Set up but do not evaluate an integral (or integrals) in terms of r that represent(s) the area of the region. That is, your final answer should be a definite integral (or integrals)....