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Calculus  II                                                             Quiz #2                                         February 24, 2003

Name____________________                       R.  Hammack                                            Score ______
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(1)   Find the following definite integrals by analyzing the graph of the integrand. Be sure to include a sketch of the graph and indicate how it gives your answer.

(a)  ∫_0^2 (| x - 1 | + 2) dx =   5  (by looking at the area of the region under the graph)

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(c)  ∫_ (3π/4)^(5π/4) tan(x) dx = A_up - A_down = 0


[Graphics:HTMLFiles/quiz2_5.gif]

(2)  The expression   Underscript[lim , n∞](Underoverscript[∑ , k = 1, arg3] ( x_k ^*)^6/( 10 + 3x_k^* ) Δx )   represents a definite integral over the interval [3, 5].   Write the definite integral. (You do not need to find its value.)   

  ∫_3^5x^6/(10 + 3x) dx


(3)  Find  ∫_1^5f(x) dx   if ∫_0^1f(x) dx = 3  and  ∫_0^5f(x) dx = 9.

One of the definite integral properties says
∫_0^5f(x) dx = ∫_0^1f(x) dx + ∫_1^5f(x) dx
9 = 3 + ∫_1^5f(x) dx
∫_1^5f(x) dx = 6