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use the limit process to find the area of the region bounded by the graph of the function f(x)=x+2 and the y axis

0 votes
use the limit process to find the area of the region bounded by the graph of the function f(x)=x+2 and the y axis over the interval of 0 less than or equal to x less than or equal to 2.(divide the interval into n even sub-intervals, and find the sum of the area of rectangles, and take the limit n approaching infinity) check your answer with the geometric formula
asked Oct 9, 2014 in CALCULUS by anonymous

2 Answers

0 votes

Number of sub intervals : n

Let the f(x) be a function and is continuous on the interval a ≤ x ≤ b.

Divide this interval into n equal width subintervals, each of which has a width of   ∆x = (b - a)/n

image

image

image

And so on ,we then have image

The Riemann sum is then image

image

 

Using Right Riemann sum, we get :

Area of the rectangle

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image

image

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image

image

image

image

image

image

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Area = 2 square units.

 

answered Oct 9, 2014 by david Expert
0 votes

Number of sub intervals : n

Let the f(x) be a function and is continuous on the interval a ≤ x ≤ b.

Divide this interval into n equal width subintervals, each of which has a width of   ∆x = (b - a)/n

image

image

image

And so on ,we then have image

The Riemann sum is then image

image

Using Right Riemann sum, we get :

Area of the rectangle

image

image

image

image

image

image

image

image
image

image

image

image

image

image

image

Area = 6 square units.

answered Oct 9, 2014 by david Expert

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