Work through the following steps to evaluate `int_0^9 (x^2+1)dx`.
a) We know that `a` =
and `b` =
.
b) Using `n` subintervals, `Delta x` =
c) Assume that the sample points in each interval are right endpoints. Find the following sample points:
`x_1 =`
`x_2 =`
`x_3 =`
In general, the `i`th sample point is `x_i =`
Note: your answer will be an expression in terms of `i` and `n`.
d) Now find the sum of the areas of `n` approximating rectangles.
Note: your answer will be an expression in terms of `n`.
`sum_(i=1)^n f(x_i) Delta x =`
e) Finally, find the exact value of the integral by letting the number of rectangles approach infinity.
`int_0^9 (x^2+1)dx` = `lim_(n rarr oo) sum_(i=1)^n f(x_i) Delta x =`
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