Math121SampleFinalSols

# Math121SampleFinalSols - FINAL(SAMPLE SOLUTIONS USE A...

This preview shows pages 1–4. Sign up to view the full content.

FINAL (SAMPLE SOLUTIONS) USE A SCIENTIFIC CALCULATOR! 1) Approximate the area under the graph of fx x () = ln from a = 4 to b = 10 by finding a Left Riemann Sum using 3 rectangles of the same width. Round off to four decimal places whenever you need to round off. (10 points) Step 1: Find D x , the width of each rectangle. D x ba n = - = - == 10 4 3 6 3 2 Step 2: Find the left breakpoints. ax x x æ Æ æ= æ Æ ++ 1 2 2 2 3 468 Step 3: Find the Left Riemann Sum. 42 62 82 2 7726 3 5835 4 1589 ◊+ () ◊ = () + ª++ = DDD ln ln ln ... 10.5150 square units Note: The exact value is closer to 11.4807.

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

View Full Document
2) Find the integrals. Simplify wherever possible. (32 points total) a) 33 12 1 5 xx d x - - () [] Ú cont. on 1,5 4 43 44 (6 points) =- = -- + 3 35 5 31 1 35 125 0 1 125 1 3 1 5 ln ln . ln ln ln ln x x ln on 1,5 3ln5 124 or ln5 124 or ln125 124 3 b) d x 2 6 4 - Ú (6 points) ux du x dx = 2 4 2 = = Ê Ë Á ˆ ¯ ˜ + =+ + Ú Ú 1 2 24 1 2 1 27 1 14 2 6 6 7 7 d x ud u u C uC 1 14 4 2 7 xC c) ex d x 3 2 61 2 +- + Ú (6 points) ux x du x xd x =+- 3 2 2 36 32 =◊ + = Ú Ú 1 3 1 3 1 3 3 2 d x ed u eC u u 1 3 3
d) ln x x dx Ú (6 points) ux du x dx = = ln 1 = () = =+ = + Ú Ú ln x x dx udu u C 1 2 2 ln 2 2 x C e) x x dx

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.

## This note was uploaded on 09/08/2011 for the course MATH 121 taught by Professor Staff during the Spring '11 term at Mesa CC.

### Page1 / 7

Math121SampleFinalSols - FINAL(SAMPLE SOLUTIONS USE A...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online