Question

Use a graphing calculator Riemann Sum (found here) to find the following Riemann sums. f(x) =...

Use a graphing calculator Riemann Sum (found here) to find the following Riemann sums.

f(x) =

2/x

  from  a = 1  to  b = 5

(a) Calculate the Riemann sum for the function for the following values of n: 10, 100, and 1000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places.

n Left Midpoint Right
10
100
1000


(b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from part (a) should approach this number. (Round your answer to three decimal places.)
square units

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
f(x) = square root x   from  a = 4  to  b = 9 (a) Calculate the Riemann sum for...
f(x) = square root x   from  a = 4  to  b = 9 (a) Calculate the Riemann sum for the function for the following values of n: 10, 100, and 1000. Use left, right, and midpoint rectangles, making a table of the answers, rounded to three decimal places. n Left Midpoint Right 10 100 1000 (b) Find the exact value of the area under the curve by evaluating an appropriate definite integral using the Fundamental Theorem. The values of the Riemann sums from...
For the function, do the following. f(x) = 1 x   from  a = 1  to  b = 2. (a)...
For the function, do the following. f(x) = 1 x   from  a = 1  to  b = 2. (a) Approximate the area under the curve from a to b by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351, rounding to three decimal places. square units (b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.   square units
f(x) = 1/x   from  a = 1  to  b = 3. (a) Approximate the area under the curve from...
f(x) = 1/x   from  a = 1  to  b = 3. (a) Approximate the area under the curve from a to b by calculating a Riemann sum using 10 rectangles. Use the method described in Example 1 on page 351,rounding to three decimal places. _____________square units (b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem. _____________square units
f(x) = 2x  from  a = 4  to  b = 5 (a) Approximate the area under the curve from a...
f(x) = 2x  from  a = 4  to  b = 5 (a) Approximate the area under the curve from a to b by calculating a Riemann sum using 5 rectangles. Use the method described in Example 1 on page 351, rounding to three decimal places.   square units (b) Find the exact area under the curve from a to b by evaluating an appropriate definite integral using the Fundamental Theorem.    square units
(a) Find the Riemann sum for f(x) = 3 sin(x), 0 ≤ x ≤ 3π/2, with...
(a) Find the Riemann sum for f(x) = 3 sin(x), 0 ≤ x ≤ 3π/2, with six terms, taking the sample points to be right endpoints. (Round your answers to six decimal places.) R6 = (b) Repeat part (a) with midpoints as the sample points. M6 = Express the limit as a definite integral on the given interval. lim n → ∞ n 7xi* + (xi*)2 Δx, [3, 8] i = 1 8 dx 3
Instructions: Approximate the following definite integrals using the indicated Riemann sums. 1. Z 9 1 x...
Instructions: Approximate the following definite integrals using the indicated Riemann sums. 1. Z 9 1 x 1 + x dx using a left-hand Riemann sum L4 with n = 4 subintervals. 2. Z 3 0 x 2 dx using a midpont Riemann sum M3 using n = 3 subintervals. 3. Z 3 1 f(x) dx using a right-hand Riemann Sum R4, with n = 4 subintervals
Use upper and lower sums (left and right Riemann sums) to approximate the area of the...
Use upper and lower sums (left and right Riemann sums) to approximate the area of the region below y =sqrt(8x) using 4 subintervals of each width. Round to three decimal places.
With a programmable calculator (or a computer), it is possible to evaluate the expressions for the...
With a programmable calculator (or a computer), it is possible to evaluate the expressions for the sums of areas of approximating rectangles, even for large values of n, using looping. (On a TI use the Is> command or a For-EndFor loop, on a Casio use Isz, on an HP or in BASIC use a FOR-NEXT loop.) Compute the sum of the areas of approximating rectangles using equal subintervals and right end points for n = 10, 30, 50, and 100....
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a...
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x, y, z) is evaluated at the center (xi, yj, zk) of the box Bijk. Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.) cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 2, 0 ≤...
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a...
In the Midpoint Rule for triple integrals we use a triple Riemann sum to approximate a triple integral over a box B, where f(x, y, z) is evaluated at the center (xi, yj, zk) of the box Bijk. Use the Midpoint Rule to estimate the value of the integral. Divide B into eight sub-boxes of equal size. (Round your answer to three decimal places.) cos(xyz) dV, where B = {(x, y, z) | 0 ≤ x ≤ 5, 0 ≤...