solution_c6pdf

solution_c6pdf - armington(kma786 – 6.1 – Stepp...

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Unformatted text preview: armington (kma786) – 6.1 – Stepp – (55860) 1 This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Express the area, A , between the graph of f and the x-axis on the interval [0 , 4] in terms of definite integral(s) when f ( x ) = 2 x- x 2 . 1. A =- integraldisplay 3 (2 x- x 2 ) dx + integraldisplay 4 3 (2 x- x 2 ) dx 2. A = integraldisplay 3 (2 x- x 2 ) dx- integraldisplay 4 3 (2 x- x 2 ) dx 3. A = integraldisplay 2 (2 x- x 2 ) dx- integraldisplay 4 2 (2 x- x 2 ) dx correct 4. A = integraldisplay 4 (2 x- x 2 ) dx 5. A =- integraldisplay 1 (2 x- x 2 ) dx + integraldisplay 4 1 (2 x- x 2 ) dx 6. A = integraldisplay 4 ( x 2- 2 x ) dx 7. A = integraldisplay 1 (2 x- x 2 ) dx- integraldisplay 4 1 (2 x- x 2 ) dx 8. A =- integraldisplay 2 (2 x- x 2 ) dx + integraldisplay 4 2 (2 x- x 2 ) dx Explanation: The graph of f is a parabola opening down- wards and crossing the x-axis at x = 0 and x = 2. Thus the required area is similar to the shaded region in the x y In terms of definite integrals, therefore, the required area is given by A = integraldisplay 2 (2 x- x 2 ) dx- integraldisplay 4 2 (2 x- x 2 ) dx ....
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solution_c6pdf - armington(kma786 – 6.1 – Stepp...

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