Unformatted text preview:
x () 8. Let R be the region bounded by the graphs of y = sin x 2 and the xaxis on the (3 pts.) interval ⎡0, π ⎤ . Which integral correctly computes the volume of the solid ⎣
⎦
formed when R is rotated around the x − axis? a) 2π π ∫ x sin ( x ) dx 2 2 0 1 () b) π ∫ sin 2 y 2 dy 0 c) π π ∫ sin ( x ) dx 2 2 d) 2π 0 π ∫ sin ( x ) dx 2 2 0 9. x2
(3 pts.) Evaluate ∫ ( 2 x ) 5 dx . 2 a) 5 x + C 2
1
c) 5 x + C 2 ln 5 x b) ( ln 5 ) 5 x + C 2 d) 1 x2
5 + C ln 5 3 MthSc 108 Test 1Version A Fall 2012 10. (3 pts.) Express 3 ln ( cos x ) − ln x 2 + 1 + ( ln 4 ) log 4 ( 3x ) as a natural logarithm of a single ( ) quantity. ( ) a) ln 3 cos x − ( x 2 + 2 ) + 12 x ⎛ ( 3x )ln 4 cos 3 x ⎞
c) ln ⎜ x2 + 1 ⎟
⎝
⎠ ⎛
cos 3 x ⎞
b) ln ⎜ 3x + 2 x +1⎟
⎝
⎠ ⎛ 3x cos 3 x ⎞
d) ln ⎜ 2
⎝ x + 1 ⎟ ⎠ 11. −1
(3 pts.) Find the slope of the line tangent to f ( x ) = sec ( 3x ) when x = 1 . 1 10 a) b) 1
8 3
c) 8 d) It is not defined. Which integral gives the correct volume when the region bounded by the x axis, 12. (3 pts.) f ( x ), g ( x ), and h( x ) is rotated about the y axis? b a) ∫ 2π xh( x ) dx b
b) ∫ 2π...
View
Full Document
 Fall '13
 Briggs
 Natural logarithm, Logarithm, dx

Click to edit the document details