--------------------------------------------------------------------------------

I am sitting here stuck on these three problems. Please help me!

1. Find an approximation for the area in the first quadrant between the x-axis and the curve y=4-(x-2)^2 using 4 equally spaced intervals and a Left Hand Rieman Sum.

Im not sure about the left hand part. But I've tried and I come up with 10 and 10.666.

2. I have graph the function of y=1/x, where x goes from 0 to 5. Using the trapexoid rule with 4 equal intervals, I must approximate the area under the curve between x=1 and x=3.

Please help.

Okay, this is what I have for the second one so far. But for some reason I keep missing it from here. I know its just a matter of calculating but I just cant get it right.

f(x) = 1/x

a = 1

b = 3

n = 4

T = [(b - a)/(2n)]*[f(x0) + 2f(x1) + 2f(x2) + ... + 2f(xn-1) + f(xn)]

T = [(3 - 1)/(2*4)]*[f(1) + 2f(3/2) + 2f(2) + 2f(5/2) + f(3)]

T = (1/4)[1 + 2(2/3) + 2(1/2) + 2(2/5) + (1/3)]

Now for the next trapezoid problem(ruler).

If the trapezoid rule is used with 5 interval,, what is the integral dx/1 + x^2 ,with limits 1,0.

Please, please help!