The triangular region in Quadrant I bounded by the x-axis, the vertical line x= 1, and the line y…

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The triangular region in Quadrant I bounded by the x-axis, the vertical line

x= 1, and the line y = 6r is rotated around the vertical line x = 1. Show that you

obtain the same volume using both the shell method and the disk method. Must show all

the steps to receive credit.

(10 points) Use integration by parts and a trig identity to evaluate the following

integral.

[csc ³0 do.

(10 points) Evaluate the following integral. All the steps must be shown in order to

receive credit.

tan x dx

(10 points) Evaluate the following integral by completing the square and trig

substitution. All the steps must be shown in order to receive credit.

dx

√x². +5+26

S (15 points) Evaluate the following integral by completing the square and trig

substitution. All the steps must be shown in order to receive credit.

5/4

1/4

dx

√4x² + 6x +1

(15 points) Evaluate the following improper integral by completing the square and trig

substitution. All the steps must be shown in order to receive credit.

dx

S. 1².

x² + 4x + 20

(20 points) Evaluate the following integral. All the steps must be shown in order to

receive credit,

-3x√1+9e-6x dx.

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