# prob7 - f ( t ) = x arcsin( x 2 + 1). 2. Find the area...

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Chapter 7 1. Section 7.1 1. Compute the general antiderivative of the function f ( x ) = x 4 e 6 x 5 . 2. Find the area underneath the function f ( x ) = 1 3 x +4 and above the x - axis on the interval [1 , 3]. 3. Compute the following indeﬁnite integral Z ( x + 1) 2 ( x - 4) 1 / 3 dx As I have been pointing out in lecture, part of the diﬃculty with integration is that it is not clear which rule to use. By the end of the chapter, you will know integration by substitution, integration by parts, integration by partial fractions, and integration by trig. substitution. So instead of going section by section, I will be putting up a list of problems that require computing indeﬁnite integrals. It is your job to ﬁgure out which rule to use. For some of the problems, there may be more than one way to proceed. You may also need to apply a few diﬀerent rules 1. Compute the general antiderivative of

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Unformatted text preview: f ( t ) = x arcsin( x 2 + 1). 2. Find the area between the line y = 50 and the function f ( x ) = x 2 e x 3 on the interval [1 , 3]. 1 3. Compute the following indeﬁnite integral Z cos 3 ( θ )sin( θ ) dθ 4. Find the general solution of the diﬀerential equation given by dy dx = 1 2 x ln(3 x ) 2. Section 7.5 1. Consider the function f ( x ) = 3+2 x 2 on the interval [1 , 4]. For each of the following pairs, state which numerical approximation overestimates Z 4 1 (3 + 2 x 2 ) dx and explain why. (a) TRAP(3) or MID(3). (b) RIGHT(3) or LEFT(3). 3. Section 7.7 1. Explain why the following improper integral diverges, or compute its value. Z 1 x ln( x ) dx You may assume that lim x → + x 2 ln( x ) = 0. This fact follows from L’Hopital’s Rule. 4. Section 7.8...
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## This note was uploaded on 09/13/2010 for the course MATH math 10b taught by Professor Reed during the Summer '10 term at UCSD.

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prob7 - f ( t ) = x arcsin( x 2 + 1). 2. Find the area...

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