104s11noans

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

• Notes
• 3

This preview shows pages 2–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern