{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

test1ans

# test1ans - Millersville University Department of...

This preview shows pages 1–3. Sign up to view the full content.

Millersville University Name Answer Key Department of Mathematics MATH 211, Calculus II , Test 1 July 28, 2009 Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses. 1. (12 points) Evaluate the following indefinite integral. x 4 ln x dx Integrate by parts letting u = ln x du = 1 x dx v = 1 5 x 5 dv = x 4 dx then x 4 ln x dx = 1 5 x 5 ln x - 1 5 x 5 1 x dx = 1 5 x 5 ln x - 1 5 x 4 dx = 1 5 x 5 ln x - 1 25 x 5 + C.

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

View Full Document
2. (13 points) Evaluate the following indefinite integral. 1 x 3 + x dx Since the integrand is a rational function, perform a partial fraction decomposition. 1 x 3 + x = 1 x ( x 2 + 1) = A x + Bx + C x 2 + 1 1 = A ( x 2 + 1) + ( Bx + C ) x Let x = 0: 1 = A (0 2 + 1) + ( B (0) + C )(0) = A 1 = 1( x 2 + 1) + ( Bx + C ) x 0 = x 2 + ( Bx + C ) x 0 = x + Bx + C Let x = 0: 0 = 0 + B (0) + C = C 0 = x + Bx + 0 0 = x + Bx 0 = 1 + B = B = - 1 Thus 1 x 3 + x dx = 1 x - x x 2 + 1 dx = 1 x dx - x x 2 + 1 dx = ln | x | -
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