Question

y = 2 x x 2 + 1 between x = 0 and x = 6 for n 1 = 6 and n 2=12. This means you will be doing two estimates for the area under the curve: one using 6 rectangles on the interval from x=0 to x=6 and a second computation using 12 rectangles on the interval from x=0 to x=12. Find the exact ar

Answer 1

For n = 1, 150

for n = 2, 1164

Explanation:

The answer for n = 1, is,

`\int_(0)^(6)(2 * x^(2) + 1)* dx`

=
`[2 * \frac {x^(3)}{3} + x]_(0)^(6)`

=150

The answer for n = 2 is,

`\int_(0)^(12)(2 * x^(2) + 1)* dx`

=
`[2 * \frac {x^(3)}{3} + x]_(0)^(12)`

= 1164