Question

How do you use Riemann sums to evaluate the area under the curve of `y = x^2 + 1` on the closed interval [0,1], with n=4 rectangles using midpoint?

Answer 1

`43/32`

Explanation:

`sum_(n=1)^4f((2n-1)/8)(1/4)=1/4(1/64+1+9/64+1+25/64+1+49/64+1)=1/4(4+84/64)=1+22/64=1+11/32=43/32`