\(\int_0^1 \frac{dx}{1+x^5} = ?\)

 

Based on the title of this thread, the estimate is supposed to be done by using a trapezoidal approximation. To do this, divide the interval [0, 1] into some number of subintervals (the more subintervals, the better the approximation).

For example, if you divide this interval into four subintervals you will have five points on the graph of your function: (0, f(0)), (.25, f(.25)), (.5, f(.5)), (.75, f(.75)), and (1, f(1)). Using each successive pairs of points, calculate the area of the trapezoid that is formed. Add the areas to get an approximation of the definite integral.

 

You're quite the mathematician, Michael!

 

Based on the title of this thread, the estimate is supposed to be done by using a trapezoidal approximation. To do this, divide the interval [0, 1] into some number of subintervals (the more subintervals, the better the approximation).

For example, if you divide this interval into four subintervals you will have five points on the graph of your function: (0, f(0)), (.25, f(.25)), (.5, f(.5)), (.75, f(.75)), and (1, f(1)). Using each successive pairs of points, calculate the area of the trapezoid that is formed. Add the areas to get an approximation of the definite integral.

Wasn't this the general concept of the LIMIT in the first place?

 

Wasn't this the general concept of the LIMIT in the first place?

The Riemann integral is defined as a limit of sums similar to the above, so to answer your question, yes, sort of.