area under the curve

**afan17** · June 24th 2008, 02:22 AM

Thanks so much.
Q1, use two rectangles to approximate the area contained between the curve and the x-axis.
use the method indicated and give your answer correct to two decimal places.
a, y=1/2xsquared between x=2 and x=3
using the right end point method

b, y=cos x between x=0 and x=pie/2
using the left endpoint method

c, y=1/2xcubed between x=1 and x=3
using the right endpoint method

**kalagota** · June 24th 2008, 05:32 AM

i'll do start the first question for you..

$y=\frac{x^2}{2}$ on $[2,3]$ using right-end-point method.

so, $a_0=2, 2+ \frac{1}{n}, 2+ \frac{2}{n}, ..., 2+ \frac{n-1}{n}, 3=a_n$

$I_k = \left[2+\frac{k-1}{n}, 2+\frac{k}{n}\right]$

so the area of the $k^{th}$ rectangle is
$A_k = f\left(2+\frac{k}{n}\right) \cdot \frac{1}{n}$
....

do the continuation..

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