Integral Approximation/Error Analysis

[rwsjyiy]

Hi so i have this problem that I am working on but I am having trouble with it.
I have to approximate the integral using either Riemann Sum or Trapezoidal sum with .2 of the actual integral. It is the integral of e^(x^2+3x+1) from 0 to 3.
Every time i try to find the n value, it ends up being huge! so it gives me a really small delta x number. Any Help?
Thanks

 

[mathman]

It is not surprising. The exponent is 19 at the end point, so the function is very large and has a steep slope. You need a very fine mesh near x=3. Is the .2 absolute or relative? If absolute, your result (n huge!) is not surprising.

 

[rwsjyiy]

it says approximate the integral within.2 and be at least as great as the actual integral

 

[deluks917]

f(x) is concave up so the trapezoidal rule always overestimates the value. I was actually surprised that I only got n = 61,000 works lol, thought it would be higher.