Left and right Riemann sums Complete the following steps for t...

Question

Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.

{Use of Tech} ƒ(𝓍) = e ˣ/₂ on [1,4]; n = 6

(d) Calculate the left and right Riemann sums.

Accepted Answer

Welcome back, everyone. Calculate the left Riemann sum for F of X equals L N X + 2 on the interval from 2 to 5 inclusive with N equals 6 subintervals. So let's begin by finding the width of each subinterval delta X. Delta X is going to be equal to 5 minus 2, divided by N, which is 6, right? So we get 3 divided by 6, which is 12. Now we're going to identify the left end points starting with X1. Since we're looking for the left end points, we begin with the lower limit of the interval. So the lower bound is 2, meaning X1 is equal to 2. X2 is going to be equal to X1 plus delta X. So we take 2 + 1/2, which is equal to 5 halves. Then we're going to take X3, which is X2 + delta X. That'd be 5 halves plus 1/2, which is equal to 3. Followed by Acts 4. We take X3 and we add Delta X, that would be 3 + 1/2. Which is 7 halves. Followed by X5, which is X4 + delta X we take. 7 halves and we add 1/2. That would be equal to 4. And finally, the sixth value X6, is X5+ delta X. Which is 4 + 1/2, and that's 9/halves. Now, our next step is to evaluate the function values. At each X, right, starting with F of X1. That'll be Alam. Off 2 + 2, which is a lot of 4. F of X2 is going to be Alan off. 5 halves plus 2. So we take a lot of 5 halves plus 2. And that's a land of nine halves. Then we take F of X3. That would be LN of 3 + 2, which is LN of 5. F of X4, which is LN of. 7 halves plus 2. This is equal to Helen of 11 halves. F of X5, which is LN of 4 + 2, that's LN of 6, and finally F of X6. That's 1 of 9 halves plus 2. Which is equal to Alan of. 13 divided by 2. Well done, and now we can apply the formula. We want to identify the sum from K equals 1 up to 6. We have 6 subintervals of F of XK multiplied by delta X. Now, Delta X is a constant, so we can factor it out, right? We get Delta X and inaries we can add our function values F of X1. Plus F of X2 and so on. Up to F of X6. So let's substitute the values delta X is equal to 1/2. Imprints we're going to add a line of 4. Plus Alan of nine halves. Plus LN of 5 plus LN of 11 divided by 2 plus LN of 6. And plus LN of 13 divided by 2. Now, let's go ahead and simplify. We're going to apply the properties of logarithms. We get 1/2 LN because we have a sum of logarithms we can simply multiply 4 by 9 halves by 5 by. 11 halves by 6, and finally multiplied by 13 divided by 2. We get one half a m of 19,305. That'll be our left rimann sum. Thank you for watching.

Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.{Use of Tech} ƒ(𝓍) = e ˣ/₂ on [1,4]; n = 6(d) Calculate the left and right Riemann sums.

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Left and right Riemann sums Complete the following steps for the given function, interval, and value of n.
{Use of Tech} ƒ(𝓍) = e ˣ/₂ on [1,4]; n = 6
(d) Calculate the left and right Riemann sums.