Find the exact area of the surface obtained by rotating the curve about the x-axis. y = 1 + ex , 0 ≤ x ≤ 9

The surface area is given by

since . To compute the integral, first let

so that , and the integral becomes

Next, let

so that . Then

so the integral becomes

Rewrite the integrand with

so that integrating the first term boils down to

where we substitute . Since

the first term in this integral contributes

The second term of the integral contributes

The antiderivative of is well-known (enough that I won't derive it here myself):

so this latter integral's contribution is

Then the surface area is

50=33x+22

step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;