Direct computation:
Parameterize the top part of the circle
by

with
, and the line segment by

with
. Then



Using the fundamental theorem of calculus:
The integral can be written as

If there happens to be a scalar function
such that
, then
is conservative and the integral is path-independent, so we only need to worry about the value of
at the path's endpoints.
This requires


So we have

which means
is indeed conservative. By the fundamental theorem, we have

Answer:
The volume of the shoe box is 420 cubic inch
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a righ rectangular prism
Given data
Length of prism l= 12inches
Width of prism w= 7 inches
Height of prism h= 5 inches
We know that the volume of a rectangular prism is expressed as
Volume =l*w*h
Volume = 12*7*5= 420in³
The circumference follows the formula
C= 2 (pi)R
R is the radius which is half the diameter when we put this into the equation we get
C = 2 (pi)(4.5)
C=28.274334
no ye puedo ayudar amigo o amiga
Answer:m
Step-by-step explanation: