indefinite integrals

Math 28, Summer 2021 Name: Quiz 5 Instructions: There are 3 problems. Read each problem carefully. Label answers appropriately. Show all your work. [6] 1) Evaluate each of the following indefinite integrals. Z a) Z b) √ x x − 2 dx (x − 1)ex dx [4] 2) Find the area bounded by f (x) = 4 − x2 and g(x) = 3x. 1 Z [10] 3) Evaluate 4 4x dx using each of the following methods. 0 a) Sketch the graph of y = 4x and find the area bounded between y = 4x and the x-axis for 0 ≤ x ≤ 4 using a geometric formula. Hint: The area A of a triangle with base b and height h is given by A = 21 b · h. b) Use the definition of the definite integral to express integral as a limit of right sums. Evaluate the limit. (Use formulas and properties included in “Sequences and Sums” supplement.) c) Use the Fundamental Theorem of Calculus to evalute the integral. 2
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