Approximate the area of the region having the given boundaries.

Question

Show the definite integral you used with your limits of integration approximated to 5 places to the right of the decimal. State your answer accurate to 5 places to the right of the decimal.  y=0, y=4-ln(1+x²)

Answer 1

area between

y=0 (x axis)

and

y = 4- ln(1+x^2)

is = integral of (-ln(1+x^2)+ 4) evaluated at limits which are where the lines intersect. one intersection point is where y =0 = 4-ln(1+x^2) or when ln(1+x^2) = 4 which is 7.32108. 2nd intersection point is -7.32108

integral of 4-ln(1+x^2) = ln(e/(1+x^2))

evaluated from about -7.32 to +7.32

is same as twice ln(e/(1+x^2) evaluated from 0 to 7.32

= area between the lines

= about 6.0000052283 square units

rounded to 5 decimal places

= 6.00000