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# Mid - converges or diverges Compute the values of the...

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MATH152 Midterm Exam 3/8/07 GIVE DETAILED AND COMPLETE SOLUTIONS. FULLY SIMPLIFY YOUR ANSWERS. NO CALCULATORS PERMITTED! 1. (13 marks) Compute (a) d dx Z arcsin x 0 e sin t dt (b) Z sec 3 x tan 3 x dx (c) Z e x 1 + e 2 x dx 2. (10 marks) Use integration by parts to compute Z cos(ln x ) dx . 3. (13 marks) Compute (a) Z x 3 9 - x 2 dx (b) Z 2 x + 5 x ( x 2 + 4 x + 5) dx 4. (12 marks) Determine for each of the following improper integrals whether it
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Unformatted text preview: converges or diverges. Compute the values of the convergent integrals. (a) Z ∞ arctan x 1 + x 2 dx (b) Z 1 ln x √ x dx 5. (12 marks) (a) Find the arc length of the curve y = √ x ( x-1 3 ) for x between 1 and 4. (b) Use integration to derive the formula for the surface area of a sphere of radius r ....
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