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Midterm1Practice

# Midterm1Practice - Midterm Practice Warning The problems...

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Unformatted text preview: Midterm Practice Warning: The problems below are meant to help you prepare for the first midterm. Doing these problems is a good thing to do. However the questions that will appear on the test may vary in type or style from the ones below. Doing nothing more than these problems is a bad thing to do. 1. (a) Approximate the area under the curve y = x 2- 1 from x = 1 to x = 4 using six equal length subintervals and left endpoints. (b) Approximate the area under the curve y = x 2- 1 from x = 1 to x = 4 using six equal length subintervals and right endpoints. (c) Compute the corresponding integral and compare your two approximations with the actual value. 2. Show that R 196884 1 1 ln( x +1) + 1 dx ≥ 196883. 3. Given that R π/ 3 24(sin( x )) 2 = 4 π- √ 27 and R π/ 2 4(sin( x )) 2 dx = π , find R π/ 2 π/ 3 (sin( x )) 2 dx . 4. Find df dx for (a) f ( x ) = R x (1 + √ u ) du ; (b) f ( x ) = R 2 x (cos( u )- √ u ) du ; (c) f ( x ) = R x 3 x 2 sin( √ u ) du , when x ≥ 0; (d) f (...
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Midterm1Practice - Midterm Practice Warning The problems...

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