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Use the Left and Right Riemann Sums with 100 rectangles to estimate the (signed) area under the curve of y=−8x+2 on the interval [0,50]. Write your answer using the sigma notation.

Use the Left and Right Riemann Sums with 100 rectangles to estimate the signed area under the curve of y8x2 on the interval 050 Write your answer using the sigm class=

Respuesta :

In order to find the left, the method is

1. Divide the interval [0,50] in 99 intervals.

2. Multiply the length of the first interval by the image of the left side of that interval

3. Do the same with all of them

4. Sum all the 99 results

On the right side, just changes 2. to the right side of the interval.

After that process, you will obtain that, the left sum is -9798.99, and the right sum is -10001.01.

In sigma notation, the left sum is

[tex]\sum_{i\mathop{=}0}^{99}[x_i-x_{i+1}]min(f(x_i),f(x_{i+1}))[/tex]

The right sum is

[tex]\sum_{i\mathop{=}1}^{100}[x_i-x_{i+1}]max{}{}f((x_i),f(x_{i+1}))[/tex]

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