Approximate

\\\\int_3^6 (1)/(x^(2))

using the midpoint rule with

n=3

(Don

t

use the fundamental theonem)\ Just express

\\\\lim_(n->\\\\infty )\\\\sum_(i=1)^n (3lnx_(i)-4x_(i)^(7)+2x_(i)^(3)cosx_(i))\\\\Delta x

as an integral on

-2,5

(Don' integrate)\ Find the area of the region bounded above by

y=x^(2)+5

, bounded below by

y=(1)/(2)x-2

, and bounded on the sides by

x=0

and

x=5

.\ Provide a formula for the volume of a hemisphere (half of a sphere) using the integration method. Do the calculation directly, not by finding the volume of a sphere and dividing it by 2

1. Approximate 36x21 using the midpoint rule with n=3 (Don't use the fundamental theonem). 2. Just express limni=1n(3lnxi4xi7+2xi3cosxi)x as an integrat on [2,5] (Don't integrate) 3. Find the area of the region bounded above by y=x2+5, bounded below by y=21x2, and bounded on the sides by x=0 and x=5. 4. Provide a formula for the volume of a hemisphere (half of a sphere) using the integration method. Do the calculation directly, not by finding the volume of a sphere and dividing it by 2