{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# math11 - Math 2153 Exam I Feb 17 2010 Name Score Read the...

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

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

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

Unformatted text preview: Math 2153, Exam I, Feb. 17, 2010 Name: Score: Read the problems carefully before you begin. Show all your work neatly and concisely, and indicate your final answer clearly. Total points = 50. 1. (8 points) Evaluate the integral integraltext ( x 2 + 1) e − x dx Solution 1 Use integration by parts twice: integraldisplay ( x 2 + 1) e − x dx parenleftbigg set u = x 2 + 1 v ′ = e − x u ′ = 2 x v =- x − x ⇒ parenrightbigg =( x 2 + 1)(- e − x )- integraldisplay 2 x (- e − x ) dx ( simplify ⇒ ) =- ( x 2 + 1) e − x + integraldisplay 2 xe − x dx parenleftbigg set u = 2 x v ′ = e − x u ′ = 2 v =- e − x ⇒ parenrightbigg =- ( x 2 + 1) e − x + bracketleftbigg 2 x (- e − x )- integraldisplay 2(- e − x ) dx bracketrightbigg ( simplify ⇒ ) =- ( x 2 + 1) e − x- 2 xe − x + integraldisplay 2 e − x dx =- ( x 2 + 1) e − x- 2 xe − x- 2 e − x + C Solution 2 Use tabular integration by parts: We have integraldisplay ( x 2 + 1) e − x dx =- ( x 2 + 1) e − x- 2 xe − x- 2 e − x + C 1 2. (8 points) Evaluate the integral integraltext sin 2 x cos 5 x dx Solution Using the identity...
View Full Document

{[ snackBarMessage ]}