e1 - 1 Z x-2 2 ± 4 1 x ² dx 2 Z ± 2 xe x 2 3 e 3 x 1 e 3...

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Math 116 Take-Home Exam 1 Directions: Do each problem correctly. Partial credit will be given for partially correct answers. You may use books, notes, and a calculator. However, you must show all work. If you use the integration capabilities of your calculator, use them only to check your answers. Furthermore, this exam is an individual eﬀort. You may not work with anyone else. Each problem is worth 25 points.
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Unformatted text preview: 1. Z ( x-2) 2 ± 4 + 1 x ² dx 2. Z ± 2 xe x 2 + 3 e 3 x +1 e 3 x +1 + 2 ² dx 3. Z 4 e √ x 2 √ x dx 4. Given that Z 2-1 f ( x ) dx = 3 and Z 2 f ( x ) dx = 1, ﬁnd Z-1 f ( x ) dx and Z 2-1 2 f ( x ) dx . 5. Find the area of the region enclosed by f ( x ) = 2 x and g ( x ) = x 2 . 6. Find the area of the region enclosed by f ( x ) = 4 x and g ( x ) = x 3 on the interval [0 , 2]....
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