
area under the curve
Thanks so much.
Q1, use two rectangles to approximate the area contained between the curve and the xaxis.
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

i'll do start the first question for you..
$\displaystyle y=\frac{x^2}{2}$ on $\displaystyle [2,3]$ using rightendpoint method.
so, $\displaystyle a_0=2, 2+ \frac{1}{n}, 2+ \frac{2}{n}, ..., 2+ \frac{n1}{n}, 3=a_n$
$\displaystyle I_k = \left[2+\frac{k1}{n}, 2+\frac{k}{n}\right]$
so the area of the $\displaystyle k^{th}$ rectangle is
$\displaystyle A_k = f\left(2+\frac{k}{n}\right) \cdot \frac{1}{n}$
....
do the continuation..