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MAC3472StudyGuideTest4

# MAC3472StudyGuideTest4 - Study Sheet for Test 4 Honors...

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Study Sheet for Test 4 Honors Calculus Keesling 11/27/07 Test on 12/4/07 1. Evaluate: (a) e x sin x ! dx (b) 1 1 ! x 2 dx " 2. Evaluate: (a) sin( x ) dx ! (b) sin( x )cos( x ) dx ! (c) sin 3 ( x ) dx ! (d) ( x 3 + 1) 5 x 2 dx ! (e) x 2 ( x 3 + 1) 5 dx ! (f) tan x ! dx 3. Evaluate: (a) cos 5 xdx ! (b) sin 2 x ! dx (c) tan 2 x ! dx (d) tan 3 ( x )sec 2 ( x ) dx ! (e) sec x ! dx (f) sin 2 x cos 3 xdx ! 4. Evaluate: (a) 1 x 2 ! 1 " dx (b) 1 x 3 ! 1 dx " (c) x + 1 3 x 2 + 2 ! dx (d) 2 x 2 ( x 2 + 1)( x 2 ! 1) " dx (e) 1 (1 + x 2 ) 2 ! dx (f) 1 a 2 + x 2 ! dx (g) 2 x 3 ( x 2 + 1)( x 2 ! 1) " dx (h) 1 a 2 + x 2 dx ! 5. Evaluate: (a) x sin x ! dx (b) e x cos x ! dx (c) x 2 cos xdx ! (d) sin 4 x dx ! (e) x ! e x sin xdx " 6. Prove the inductive formula for integrating sin 2 n ( x ) . sin 2 n ( x ) dx ! = " sin 2 n " 1 ( x )cos( x ) 2 n + 2 n " 1 2 n sin 2 n " 2 ( x ) dx ! 7. Prove the inductive formula for integrating tan 2 n ( x ) . tan 2 n ( x ) dx = tan 2 n ! 1 ( x ) 2 n ! 1 " ! tan 2 n ! 2 ( x ) dx " 8. Evaluate: (a) a 2 + b 2 x 2 dx ! (b) 1 x 2 ! a 2 dx " (c) 1 ( a 2 + x 2 ) 3 ! dx (d) x x 2 ! 5 " dx (e) 1 1 ! x 2 dx " 9. Use the Romberg Integration program on your calculator to evaluate the integral e x dx 1 2 !

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MAC3472StudyGuideTest4 - Study Sheet for Test 4 Honors...

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