Evaluate the following...

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Math 2B Single Variable Calculus Midterm 1 (v1) Fall 2016 Name: Student Id#: Discussion Class Time: Total marks = 50 (per question in brackets) No calculators or other electronic devices Unless otherwise stated, include all your working for full credit Try all parts of every question, even if you can’t do the first part
Question Marks 1 /14 2 /6 3 /7 4 /15 5 /8 Total /50 1. Evaluate the following integrals: (a) Z π 0 3 x 2 + sin x d x (3) (b) Z 2 x 1 + x 2 d x (3)
(c) Z ( x + x - 1 ) 2 d x (4) (d) Z e 1 1 x ( ln x ) 2 d x (4)
2. Evaluate the following: (a) d d x Z x 2 4 sin ( cos t ) d t (3) (b) d d y Z 6 y x 3 - 3 x d x (3)
3. Consider the Riemann sum 8 i = 1 1 + i 4 3 1 4 (a) Find a function f and an interval [ a , b ] such that the Riemann sum approximates the area under the curve y = f ( x ) between x = a and x = b . (4) (b) Evaluate the area in described in part (a). (3)
4. The region

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