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January 27, 2015

January 27, 2015

Posted by **Eric** on Wednesday, May 15, 2013 at 10:51am.

this is all for definite integral

i just know x1=1.4, x2=1.8, x3=2.2, x4=2.6, x5=3.0

how do i continue

- definite integral -
**Steve**, Wednesday, May 15, 2013 at 11:07amyou're halfway there. We approximate the integral by adding up the areas of the rectangles. Since the width of each rectangle is 0.4, all we have to do is evaluate f(x) at some point in each interval and multiply.

Usually the left side, middle, or right side of the rectangle is chosen, but as the actual value of the integral is the limit as the width decreases to zero, it doesn't really matter where in the interval f(x) is evaluated.

Since you have specified inscribed rectangles, and since 1/x is concave upward for x>0, we will want the right end of each interval. (If that's not clear, sketch the curve and see where the rectangles intersect the curve.)

So, just add up

0.4 (f(1.4)+f(1.8)+...+f(3))

0.4 (.714+.556+.455+.385+.333)

0.4 * 2.442

= 0.977

Since our rectangles are all under the curve, our estimate will be low.

Actual value: 1.0986

- definite integral -
**Eric**, Wednesday, May 15, 2013 at 11:09amwow I didn't think it was so simple. thank you !

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