{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# AnswersCalcHW3 - Version 010 – Homework 3 – Odell...

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: Version 010 – Homework 3 – Odell – (58340) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The graph of f is shown in the figure 2 4 6 8 2 4 6 If F is an anti-derivative of f and integraldisplay 8 2 f ( x ) dx = 49 2 , find the value of F (8)- F (1). 1. F (8)- F (1) = 28 2. F (8)- F (1) = 119 4 3. F (8)- F (1) = 217 8 correct 4. F (8)- F (1) = 245 8 5. F (8)- F (1) = 231 8 Explanation: We already know that the area under the graph on the interval 2 ≤ x ≤ 8 is equal to 49 2 , alternatively, by the Fundamental Theorem of Calculus we can say that F (8)- F (2) = 49 2 . On the other hand, integraldisplay 8 1 f ( x ) dx = integraldisplay 2 1 f ( x ) dx + integraldisplay 8 2 f ( x ) dx. Thus we need to find integraldisplay 2 1 f ( x ) dx = F (2)- F (1) . Now integraldisplay 2 1 f ( x ) dx = integraldisplay 2 1 7 4 x dx = 7 8 bracketleftBig x 2 bracketrightBig 2 1 = 21 8 . Consequently, F (8)- F (1) = 49 2 + 21 8 = 217 8 . keywords: velocity, distance, graph analysis, fundamental theorem 002 10.0 points Calculate the indefinite integral I = integraldisplay (4- √ x )(5 + √ x ) dx . 1. I = 4 x- 2 3 x √ x + 1 2 x 2 + C 2. I = 20 x + √ x- 1 2 x 2 + C 3. I = 20 x- 2 3 x √ x- 1 2 x 2 + C correct 4. I = 4 x + √ x- 1 2 x 2 + C 5. I = 20 x- 2 3 x √ x + 1 2 x 2 + C 6. I = 4 x + 2 3 x √ x- 1 2 x 2 + C Explanation: After expansion (4- √ x )(5 + √ x ) = 20- √ x- x . Version 010 – Homework 3 – Odell – (58340) 2 Thus I = integraldisplay ( 20- √ x- x ) dx = 20 x- 2 3 x √ x- 1 2 x 2 + C . Consequently, I = 20 x- 2 3 x √ x- 1 2 x 2 + C . 003 10.0 points Evaluate the definite integral I = integraldisplay π 3 3 sin 2 x- 2 cos 2 x cos x dx . 1. I = 6 + √ 2 2. I = 6 + √ 3 3. I = 6- √ 3 4. I = 3- √ 2 5. I = 3 + √ 3 6. I = 3- √ 3 correct Explanation: Since sin 2 x = 2 sin x cos x , the integrand can be rewritten as 6 sin x cos x- 2 cos 2 x cos x = 2(3 sin x- cos x ) . Thus I = 2 integraldisplay π 3 (3 sin x- cos x ) dx = 2 bracketleftBig- 3 cos x- sin x bracketrightBig π 3 = 2 parenleftBigg- 3 2- √ 3 2 parenrightBigg + 6 . Consequently, I = 3- √ 3 . 004 10.0 points Evaluate the integral I = integraldisplay 2 d dx (3 + x 2 ) 1 / 2 dx. 1. I = √ 7 + √ 3 2. I = √ 7 3. I = √ 3- √ 7 4. I = √ 3 5. I = √ 7- √ 3 correct Explanation: As an indefinite integral, integraldisplay d dx (3 + x 2 ) 1 / 2 dx = (3 + x 2 ) 1 / 2 + C where C is an arbitrary constant. Thus integraldisplay 2 d dx (3 + x 2 ) 1 / 2 dx = bracketleftBig (3 + x 2 ) 1 / 2 bracketrightBig 2 . Consequently, I = √ 7- √ 3 . 005 10.0 points Determine the indefinite integral I = integraldisplay 4- cos 2 θ cos 2 θ dθ ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 12

AnswersCalcHW3 - Version 010 – Homework 3 – Odell...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online