19b-quiz-midterm-v1-solutions.pdf - Math 19B Calculus for...

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Math 19B: Calculus for Science, Engineering and Mathematics FALL 2017 TA Suzana Milea Quiz (5.1 - 7.2) - Solutions 1. (5 pts) Evaluate R π 2 0 cos 3 ( x ) sin( x ) dx. Let u = cos( x ) . Then du = - sin( x ) dx . If x = 0 then u = cos(0) = 1 . If x = π 2 then u = cos( π 2 ) = 0 . Hence R π 2 0 cos 3 ( x ) sin( x ) dx = R 0 1 ( - u 3 ) du = - u 4 4 0 1 = - 0 + 1 4 = 1 4 . 2. (5 pts) Use the Fundamental Theorem of Calculus (Part II) to find the derivative of the following function; justify your answers by showing your calculations.
3. (5 pts)

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