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

step-by-step explanation:

so first find out how much each is worth.

quarter= 25 cents

dime= 10 cents

pennies= 1 cent

then multiply each by how much each is worth.

200                     150                   300

x                         x                     x   1

  25                       10              

                                  300

1000                     1500

+                          

4000                                      

5000                                  

then count 2 from the back and add a period.

$50.00

$15.00

$3.00

and then add them

  $50.00

+

  $15.00

+

    $3.00

$68.00

so sunghee has $68.00

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step-by-step explanation: