{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

q2solns

# q2solns - Mathematics 104 Quiz 2 Friday 1 Find dx(x 2(x2 1...

This preview shows page 1. Sign up to view the full content.

Mathematics 104 Quiz 2, Friday, Feb 22, 2008 1. Find integraldisplay dx ( x + 2)( x 2 + 1) . 1 ( x + 2)( x 2 + 1) = A x + 2 + Bx + C x 2 + 1 Ax 2 + A + Bx 2 + 2 Bx + Cx + 2 C = 1 + 0 x + 0 x 2 . This gives the system A + B = 0, 2 B + C = 0 and A + 2 C = 1 which we solve to find A = 1 / 5, B = - 1 / 5 and C = 2 / 5. So our integral becomes integraldisplay 1 / 5 x + 2 dx + 1 5 integraldisplay 2 - x x 2 + 1 = 1 5 ln | x + 2 | - 1 10 ln( x 2 + 1) + 2 5 arctan x + C 2. Find integraldisplay x 2 x 2 - x - 12 dx . The rational function we need to integrate is not proper. We can rewrite the integrand as x 2 x 2 - x - 12 = x 2 - x - 12 x 2 - x - 12 + x + 12 x 2 - x - 12 = 1 + x + 12 ( x - 4)( x + 3) So our integral becomes integraldisplay 1 dx + integraldisplay A x - 4 dx + integraldisplay B x + 3 dx where A ( x + 3) + B ( x - 4) = x + 12 Substituting x = - 3 and x = 4 gives A = 16 / 7 and B = - 9 / 7. So our answer is x + 16
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