Worksheet 2 - Group Name Math 231 ABCE Spring 2012 Worksheet 2 Jan 23\/24 1 Do the following integrals via integration by parts(a arctan(x dx(b x2 ln x

Worksheet 2 - Group Name Math 231 ABCE Spring 2012...

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Group: Name: Math 231 ABCE. Spring 2012. Worksheet 2. Jan. 23/24 1.Do the following integrals via integration by parts(a)Zarctan(x)dx(b)Zx2lnx dx(c)Zx3ex2dx.(Hint:Either integrate by parts directly, or make a substitution to reduce to a simpler integral.)2.The identities sin 2x= 2 sinxcosxand cos2(x) =1+cos(2x)2are useful for (a) and (b).Zsin(x) sin(2x)dx (a)(b)Zcos4(x)dx(c)Zcos3(x) sin2(x)dx
(d) Z sin 3 ( x ) cos x dx 3. In this problem you will find Z sin 2 ( x ) dx without using the formula sin 2 ( x ) = 1 - cos(2 x ) 2 . (a) Integrate by parts to get a formula for Z sin 2 ( x ) dx which involves Z cos 2 ( x ) dx . (b) Use part (a) and the identity cos 2 ( x ) + sin 2 ( x ) = 1 to evaluate Z sin 2 ( x ) dx . 4. Do as many of these as you can. Solutions will be posted. (a) Z e x dx ( Hint: start by substituting t = x ). (b) Z (ln x ) 3 dx . (c) Z e x (cos x + sin x ) dx . (d) Z π/ 2 - π/ 2 sin 7 x dx ( Hint: you can do this in your head.)

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