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Evaluate the following integral by completing the square and using a substitution to reduce it...
Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8)...
Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8) (t/2-7T/8) and the cos t-axis on [7T/8,15/ 8] with n 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see figure) 0.5 27 2 The approximate area of the region is (Round to two decimal places as needed.) N| a.
Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8) (t/2-7T/8) and...
t = 9:2-7x: @ Approidmate the area of the region bounded by the graph of f(t)...
t = 9:2-7x: @ Approidmate the area of the region bounded by the graph of f(t) = cos (t/2-71/) and the t-bode on [3./4.7x4 with n = 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle see figura) The approximate area of the region is (Round ta wo decimal places as needed t = 9:2-7x: @ Approidmate the area of the region bounded by the graph of f(t) = cos (t/2-71/) and the t-bode...
Find the indicated Midpoint Rule approximation to the following integral. 12 S22 2x dx using n=1,...
Find the indicated Midpoint Rule approximation to the following integral. 12 S22 2x dx using n=1, 2, and 4 subintervals 4 12 The Midpoint Rule approximation of S xx? dx with n= 1 subinterval is (Round to three decimal places as needed.)
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4...
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4 and M4 for the given interval. Step 1 The Midpoint Rule says that b f(x) dx = Mn Ax[f(+1) + f(22) + ... + f(n)] with ax = . b - a + n a 1 We need to estimate 6 2 cos(x2) dx with n = 4 subintervals. For this, 1 - 0 Ax = 4 = 1/4 1/4 Step 2 Let žų...
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using...
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a midpoint Riemann sum· illustrate the solution geometrically. C. Divide [04] into n = 4 subintervals and...
EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral. dx...
EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral. dx х SOLUTION The endpoints of the subintervals are 1, 1.6, 2.2, 2.8, 3.4, and 4, so the midpoints are 1.3, 1.9, 2.5, 3.1, and width of the subintervals is Ax = (4 - 175 so the Midpoint Rule gives The 1.9* 2s 313) dx Ax[f(1.3) + (1.9) + (2.5) + F(3.1) + f(3.7)] -0.06 2 + 1.3 2.5 3.1 . (Round your answer to...
8. (7 points) Evaluate the indefinite integral using a substitution. State the substitution and show all...
8. (7 points) Evaluate the indefinite integral using a substitution. State the substitution and show all work to justify your result for credit. dx V1 - 4x2 sin-1(2x)
All of 10 questions, please. 1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the...
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
2. Write the limit of the Riemann sums as a definite integral. plz !!! Cancel 1....
2. Write the limit of the Riemann sums as a definite
integral.
plz !!!
Cancel 1. f(x) = x3 Find the Riemann sum for function f. -2 < x < 3 partitioned into 5 equal subintervals for which u; is the left endpoint of each subinterval. 9 1 • dx a. 성 - 1 b. Sutra ( + r + 6)dx - 3 2. C. { (-6x (-6x3 - 3x² + 2x)dx -2
2x 3) Let f(x) = 3V9+x2 a) Evaluate the definite integral 1393 f(x)dx, using Trigonometric substitution....
2x 3) Let f(x) = 3V9+x2 a) Evaluate the definite integral 1393 f(x)dx, using Trigonometric substitution. b) Find f(x)dx, using Trigonometric substitution. c) Is there any other way to compute the integral of part b). Explain. If yes, then show the calculations.
Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8) (t/2-7T/8) and the cos t-axis on [7T/8,15/ 8] with n 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle (see figure) 0.5 27 2 The approximate area of the region is (Round to two decimal places as needed.) N| a.
Approximate the area of the region bounded by the graph of f(t) f(t) cos(t/2-7t / 8) (t/2-7T/8) and...
t = 9:2-7x: @ Approidmate the area of the region bounded by the graph of f(t) = cos (t/2-71/) and the t-bode on [3./4.7x4 with n = 4 subintervals. Use the midpoint of each subinterval to determine the height of each rectangle see figura) The approximate area of the region is (Round ta wo decimal places as needed t = 9:2-7x: @ Approidmate the area of the region bounded by the graph of f(t) = cos (t/2-71/) and the t-bode...
Find the indicated Midpoint Rule approximation to the following integral. 12 S22 2x dx using n=1, 2, and 4 subintervals 4 12 The Midpoint Rule approximation of S xx? dx with n= 1 subinterval is (Round to three decimal places as needed.)
Given the integral below, do the following. 2 cos(x2) dx Exercise (a) Find the approximations T4 and M4 for the given interval. Step 1 The Midpoint Rule says that b f(x) dx = Mn Ax[f(+1) + f(22) + ... + f(n)] with ax = . b - a + n a 1 We need to estimate 6 2 cos(x2) dx with n = 4 subintervals. For this, 1 - 0 Ax = 4 = 1/4 1/4 Step 2 Let žų...
Estimate the area of the region bounded by the graph of f(x)-x + 2 and the x-axis on [0,4] in the following ways a. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,4] into n = 4 subintervals and approximate the area of the region using a midpoint Riemann sum· illustrate the solution geometrically. C. Divide [04] into n = 4 subintervals and...
EXAMPLE 5 Use the Midpoint Rule with n = 5 to approximate the following integral. dx х SOLUTION The endpoints of the subintervals are 1, 1.6, 2.2, 2.8, 3.4, and 4, so the midpoints are 1.3, 1.9, 2.5, 3.1, and width of the subintervals is Ax = (4 - 175 so the Midpoint Rule gives The 1.9* 2s 313) dx Ax[f(1.3) + (1.9) + (2.5) + F(3.1) + f(3.7)] -0.06 2 + 1.3 2.5 3.1 . (Round your answer to...
8. (7 points) Evaluate the indefinite integral using a substitution. State the substitution and show all work to justify your result for credit. dx V1 - 4x2 sin-1(2x)
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
2. Write the limit of the Riemann sums as a definite
integral.
plz !!!
Cancel 1. f(x) = x3 Find the Riemann sum for function f. -2 < x < 3 partitioned into 5 equal subintervals for which u; is the left endpoint of each subinterval. 9 1 • dx a. 성 - 1 b. Sutra ( + r + 6)dx - 3 2. C. { (-6x (-6x3 - 3x² + 2x)dx -2
2x 3) Let f(x) = 3V9+x2 a) Evaluate the definite integral 1393 f(x)dx, using Trigonometric substitution. b) Find f(x)dx, using Trigonometric substitution. c) Is there any other way to compute the integral of part b). Explain. If yes, then show the calculations.
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