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

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

the answer is c just got it on ed

step-by-step explanation: