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2. Evaluate the following indefinite integrals: (a) vel V=(x+2) dx ET (b) 3. Evaluate the following...
cannot figure out how to write the integrals for this problem #2 1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-...
cannot figure out how to write the integrals for this
problem #2
1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-80% 3 3 2 Let fix)-. Let R be the region in the first quadrant bounded by the gruph of y - f(x) and the vertical line x # l, as shown in the figure above. (a) Write but do...
Q3 1. For the following, in (a) sketch the graphs of the functions and in (a)...
Q3
1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r =...
4. Sketch the region enclosed by the curves y = x, y = 4x, y =...
4. Sketch the region enclosed by the curves y = x, y = 4x, y = -x +2, and find its area by any method. 5. Find the volume of the solid generated when the region between the graphs of f(x) = 1 + x2 and g(x) = x over the interval (0, 2) is revolved about the x- axis.
Question 1 (2 points) ✓ Saved The base of a solid, s, is the region enclosed...
Question 1 (2 points) ✓ Saved The base of a solid, s, is the region enclosed by the graph of y = 2 - 22 and the coordinate axes. If all plane cross sections perpendicular to the y-axis are squares, then the volume of S is given by Question 2 (2 points) The region enclosed by the graph of y = 1 and y=sin(x) from X = 0 to x = is rotated about about the x-axis. What is the...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
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...
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.
Q14 Find the distance from x=3 to x = 8 on the graph of y als...
Q14 Find the distance from x=3 to x = 8 on the graph of y als Find the area of the surface generated by rotating y = 25*56 about the y-axis. Bonus: (1) Draw the region that is represented by the following definite integral which represents the volume of a solid generated by rotating the region about some axis. Be sure to label the curves and the axis of revolution: 2 (2 - y)- y)dy
6. [10 points] Consider the function f(x) = 2 + cose over the interval (1,6), where...
6. [10 points] Consider the function f(x) = 2 + cose over the interval (1,6), where I is measured in radians. Let S be the region that is bounded above by the graph of f(x), below by the 2-axis, on the left by the line = 1, and on the right by the line = 6. This question concerns the process of approximating, and exactly calculating, the volume of the solid that is obtained when S is rotated around the...
Find the area of the region in the XY-plane enclosed by y = 3−x and x...
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.
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find ...
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the region R in the ry-plane bounded by the curve y --x? +2x and the line y - x-2, while the top of the solid is bounded by the surface z xy e"
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the...
cannot figure out how to write the integrals for this
problem #2
1. If glx) -2x and fx) - , find the area of the region enclosed by the two graphs. Show a work for full credit. (4 pts) 2. A:12-80% 3 3 2 Let fix)-. Let R be the region in the first quadrant bounded by the gruph of y - f(x) and the vertical line x # l, as shown in the figure above. (a) Write but do...
Q3
1. For the following, in (a) sketch the graphs of the functions and in (a) and (b) find the areas as indicated (a) the area bounded by y = f(x) = x2 - 4x + 5 and y = g(2) = 2x - 3. (b) the area of the region that is common to r= 3 cos(0) and r = sin(). See sketch below. 2. Consider the region bounded by y? = 4, y = 2 and r =...
4. Sketch the region enclosed by the curves y = x, y = 4x, y = -x +2, and find its area by any method. 5. Find the volume of the solid generated when the region between the graphs of f(x) = 1 + x2 and g(x) = x over the interval (0, 2) is revolved about the x- axis.
Question 1 (2 points) ✓ Saved The base of a solid, s, is the region enclosed by the graph of y = 2 - 22 and the coordinate axes. If all plane cross sections perpendicular to the y-axis are squares, then the volume of S is given by Question 2 (2 points) The region enclosed by the graph of y = 1 and y=sin(x) from X = 0 to x = is rotated about about the x-axis. What is the...
4. (Calculator) Let R be the region bounded by the graphs of f(x)= 20+x-x2 and g(x)=x-5x. (a) Find the area of R. (b) A vertical line x k divides R into two regions of equal area. Write, but do not solve, an equation that could be solved to find the value of k (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse...
Q14 Find the distance from x=3 to x = 8 on the graph of y als Find the area of the surface generated by rotating y = 25*56 about the y-axis. Bonus: (1) Draw the region that is represented by the following definite integral which represents the volume of a solid generated by rotating the region about some axis. Be sure to label the curves and the axis of revolution: 2 (2 - y)- y)dy
6. [10 points] Consider the function f(x) = 2 + cose over the interval (1,6), where I is measured in radians. Let S be the region that is bounded above by the graph of f(x), below by the 2-axis, on the left by the line = 1, and on the right by the line = 6. This question concerns the process of approximating, and exactly calculating, the volume of the solid that is obtained when S is rotated around the...
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the region R in the ry-plane bounded by the curve y --x? +2x and the line y - x-2, while the top of the solid is bounded by the surface z xy e"
Exercise 6. (17pts) In this exercise use double integrals. a. Evaluate the integralj"fo/ b. Find the volume of the solid whose base is the...
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