Integral Approximation and Error Analysis

[rwsjyiy]

Homework Statement

Approximation of e^(x^2+3x+1) from 0 to 3 within .2 of the actual integral.

Homework Equations

Riemann Sum or Trapezoidal. (We haven't learned Taylor yet).

The Attempt at a Solution

Last n value i found was 148068 which gave me a delta x of 3/148068...im very confused.

 

[kurt.physics]

Can someone help me solve this? I have the right answer for the integral (1953.2) but I'm not sure how to get there.So I am doing a right Riemann Sum: $$\sum_{i=1}^n f(x_i) \Delta x$$Where $$\Delta x = \frac{b-a}{n}$$ and $$f(x_i) = e^{x^2+3x+1}$$I'm given the interval [0, 3], so b = 3 and a = 0. Also, I'm told to approximate the integral within .2 of the actual integral. That means my goal is to make my calculation within .2 of 1953.2. So I can start off by choosing an arbitrary n value. Let's say n = 10. Then $$\Delta x = \frac{3-0}{10} = \frac{3}{10} = 0.3$$Now I just need to evaluate the function at each point on the interval and then multiply by the delta x. $$f(x_1) \Delta x = e^{0^2+3(0)+1}(0.3) = e^1(0.3) = 2.71828(0.3) = 0.815484$$$$f(x_2) \Delta x = e^{(0.3)^2+3(0.3)+1}(0.3) = e^1.51(0.3) = 4.52(0.3) = 1.3560$$$$f(x_3) \Delta x = e^{(0.6)^2+3(0.6)+1}(0.3) = e^2.51(0.3) = 12.2(0.3) = 3.66$$$$f(x_4) \Delta x = e^{(0.9)^2+3(0.9)+1}(0.3) = e^3.51(0.3) = 33.4(0.3) = 10.02$$$$f(x_5) \Delta x = e^{(1.2)^2+