Riemann Sum from Indefinite Integral

[Ocasta]

Homework Statement

Consider the integral,

$\int _3 ^7 (\frac{3}{x} + 2) dx$

a) Find the Riemann Sum for this integral using right endpoints and n=4.

b) Find the Riemann Sum for this integral using left endpoints and n=4.

Homework Equations

The sum,
$\sum^{n = 4} (\frac{3}{x} + 2)$

The graph,

f(x) (white)
x = 3 (blue)
x = 7 (blue)
y = 3 (yellow)
y = f(7) (red)

The Attempt at a Solution

The right endpoint would be (7, f(7))
The product of the sum would be the area of the box, so
$f(7) * 4$
(this answer is in an acceptable format for my teacher)

The left endpoint would be (3,F(3))
The product of the sum would be the area of the box, so
$f(3) * 4 = 12$

But I'm wrong, evidently.

Thanks in advance, guys!

 

[dynamicsolo]

The condition n = 4 in the two parts of the problem means that you are to divide the interval from x = 3 to x = 7 into four equal parts, and then find the total area of the four rectangles you are to construct for the Riemann sum, using either the "Right Endpoint" or "Left Endpoint Rule".

 

[Ocasta]

You're right! I can't believe I forgot this. Thanks dynamicsolo!

btw, That's some great advice in your signature.

For future reference,

$\sum_i^4 \frac{3}{x} + 2 \rightarrow$

Right
$(i)(\frac{n}{7-3})[f(3) + f(4) + f(5) + f(6)]$

Left
$(i)(\frac{n}{7-3})[f(7) + f(4) + f(5) + f(6)]$