Friday

October 24, 2014

October 24, 2014

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 !

**Answer this Question**

**Related Questions**

Riemann Sums - Use the Riemann Sums corresponding to 5 inscribed rectangles of ...

Calculus - Can someone explain to me how to do these? Given the following ...

calculus - There are four integrals: 1) definite integral x/(1+x^4)dx b/w ...

calculus - There are four integrals: 1) definite integral x/(1+x^4)dx b/w ...

Calc - If we know that the definite integral from -6 to -3 of f(x) equals 6, the...

Calculus - Would someone clarify this for me... Is antiderivatives just another ...

Calc - (1/1+(4/n))(4/n)+(1/1+(8/n))(4/n)+(1/1+(12/n))(4/n)+....+(1/1+(4n/n))(4/n...

Calculus - Use the symmetry of the graphs of the sine and cosine functions as an...

Calculus II/III - A. Find the integral of the following function. Integral of (x...

math - Note: You can get full credit for this problem by just answering the last...