/5 pts Use the Fundamental Theorem of Calculus Part II...

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Math 19B: Calculus for Science, Engineering and Mathematics FALL 2017 TA Suzana Milea Quiz (5.1 - 7.2) Student ID: First Name: Last Name: 1. ( /5 pts) Evaluate R π 2 0 cos 3 ( x ) sin( x ) dx. 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. f ( x ) = Z x 2 x tan( t ) dt 3. ( /5 pts) Find the area bounded by the parabola y = x 2 + 2 and the line y = 2 x + 5. 4. ( /5 pts) Find the volume V of the solid obtained by rotating the region above the graph of y = x 2 + 5 and below y = 14 for 0 x 3 about the line x = - 2. 5. ( /5 pts) Evaluate the definite integral. Z π 0 ( x + 1) sin( x ) dx 6. ( /5 pts) Evaluate using methods similar to those that apply to R tan m ( x ) sec n ( x ). Z cot 8 ( x ) csc 2 ( x ) dx University of California Santa Cruz Math 19B: Calculus for Science, Engineering and Mathematics Fall 2017 T.A. Suzana Milea Quiz (5.1 - 7.2)

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