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

Use the Riemann Sums corresponding to 5 inscribed rectangles of equal width to approximate the integral a= 1, b= 3, (1/x)dx

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 - , Wednesday, May 15, 2013 at 11:07am

    you'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 - , Wednesday, May 15, 2013 at 11:09am

    wow I didn't think it was so simple. thank you !

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