Answer:
Rn ≈ 0.6345
Ln ≈ 0.7595
Step-by-step explanation:
The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.
It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:
x = -1, -.25, 0.50, 1.25, 2
Of course, the spreadsheet can easily compute the sum of products for you.
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The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:
Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)
Rn ≈ 0.6345
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The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:
Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)
Ln ≈ 0.7595
_____
It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).
Step-by-step explanation:
Rn ≈ 0.6345
Ln ≈ 0.7595
Step-by-step explanation:
The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.
It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:
x = -1, -.25, 0.50, 1.25, 2
Of course, the spreadsheet can easily compute the sum of products for you.
__
The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:
Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)
Rn ≈ 0.6345
__
The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:
Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)
Ln ≈ 0.7595
_____
It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).
