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Consider the graph of y lncos x between x 0 and x 1

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10. Consider the graph of y = ln(cos( x )) between x = 0 and x = 1. Which of the following integrals corresponds to the surface area of the object obtained by rotating this graph about the x -axis? (a) integraldisplay 1 0 2 π radicalbig 1 + ln(cos( x )) 2 dx (b) integraldisplay 1 0 2 π ln(sin( x )) radicalbig 1 + sec 2 ( x ) dx (c) integraldisplay 1 0 2 π cos( x ) ln(sin( x )) dx (d) integraldisplay 1 0 2 π sec( x ) ln(cos( x )) dx (e) integraldisplay 1 0 2 πx 2 sin( x ) cos( x ) ln( x ) dx (f) integraldisplay 1 0 2 π sin 2 ( x ) radicalbig 1 + ln( x ) 2 dx 11. A certain random variable has probability density function f ( x ) given by f ( x ) = xe x for x > 0, and f ( x ) = 0 for x 0. Find the mean of this random variable. 12. Suppose that a sequence { a n } converges to π . Then the sequence { cos( a n ) } 13. Suppose that a series n =1 a n converges to e , where each a n > 0. Then the series n =1 1 /a n
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