integrals

• Nov 18th 2008, 05:36 PM
thecount
integrals
Suppose f(x) > 0 on [2, 5].
(1)*f(2) + (1)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

True or False

Suppose f(x) > 0 on [2, 5].
(1.5)*f(2) + (1.5)*f(5) gives an estimate of the area under the graph of f.

True or False

Suppose f(x) > 0 on [2, 5].
(2)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

True or False

im confused...
• Nov 18th 2008, 05:55 PM
TheEmptySet
Quote:

Originally Posted by thecount
Suppose f(x) > 0 on [2, 5].
(1)*f(2) + (1)*f(3) + (1)*f(4) gives an estimate of the area under the graph of f.

True or False

im confused...

Using the definition of the Riemann sum with the left end points of each of the subdivisions.

$\Delta x=\frac{b-a}{n}=\frac{5-2}{3}=1$ and

$x_i=a+i\Delta x$ for $i=0,1,2$ since we are using the left endpoints so we get

$\int_{2}^{5}f(x)dx \approx \sum_{i=0}^{2}f(x_i)\Delta x=f(2)+f(3)+f(4)$

think about the other ones and see if they fit other methods you know (Clapping)