Question

How do you find the area under the curve `f(x) = x^(2) + 1` over [0,1] with n = 4 using the midpoint of each subinterval?

Answer 1

`85/64`

Explanation:

The four interval would be`0 to 1/4 , 1/4 to 1/2, 1/2 to 3/4 and 3/4 to 1.`

The mid points would be`1/2, 3/8, 5/8,7/8`

Area would be `1/4* f(1/8) +1/4* f(3/8) + 1/4 * f(5/8) +1/*(f7/8)`

= `1/4{ f(1/8)+f(3/8) +f(5/8)+f(7/8)}`

= `1/4 (65/64+ 73/64+89/64 +113/64)`

=`1/4(340/64)`
= `85/64`