# Final Exam Review Solutions - Math 2212 Final Exam Review...

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Math 2212, Final Exam Review Sheet Instructions The final exam is comprehensive; it will test concepts covered throughout the entire course. In order to prepare for this test please refamiliarize yourself with the concepts and topics covered on the first three exams and the material covered after the third exam. It is best to master the types of problems that are on this review sheet and the study material provided for the first three exams. Please note that this sheet is not comprehensive in the types of problems that may arise on the final exam. You are encouraged to work the following practice problems until you can do them correctly on your own (without any notes, answers, or guidance). This level of expertise and confidence is ideal for entering the exam. Also, be sure to revisit your written homework assignments, practice problems from class, and the suggested problems posted for the course on uLearn. Problems 1. Evaluate the following integrals ( a ) Z ( x 2 + 1) 2 x 3 dx ( b ) Z 2 - 3 3 2 x + 7 dx ( c ) Z π/ 2 0 sin(3 θ ) cos(3 θ ) d θ ( d ) Z t + 1 ( t + 4)( t - 3) dt ( e ) Z x ln x dx ( f ) Z xe 2 x dx ( g ) Z cos 2 (2 θ ) d θ ( h ) Z 1 / 2 0 dx 1 - x 2 ( i ) Z 3 5 + x 2 dx ( j ) Z 2 a 5 r dr ( k ) Z tan 5 ( θ ) sec 2 ( θ ) d θ ( l ) Z π/ 3 π/ 6 cot( x ) dx ( m ) Z sin 5 x dx ( n ) Z x + 1 x 2 + 1 dx ( o ) Z 4 s 2 + s - 2 s 2 ( s - 2) ds ( p ) Z 2 x 2 + x + 1 ( x - 1)( x 2 + 1) dx
( a ) 1 2 x 2 + 2 ln | x | - 1 2 x - 2 ( b ) 3 2 ln(11) ( c ) - 1 6 ( d ) 3 7 ln | t + 4 | + 4 7 ln | t - 3 | + C ( e ) 1 2 x 2 ln x - 1 4 x 2 + C ( f ) 1 2 xe 2 x - 1 4 e 2 x + C ( g ) 1 2 θ + 1 8 sin(4 θ ) + C ( h ) π 6 ( i ) 3 5 tan - 1 x 5 ! + C ( j ) 2 a 5 r 5 ln a + C ( k ) 1 6 tan 6 θ + C ( l ) ln( 3) = ln(3) 2 ( m ) - cos x + 2 3 cos 3 x - 1 5 cos 5 x + C ( n ) 1 2 ln( x 2 + 1) + tan - 1 ( x ) + C ( o ) - 1 s + 4 ln | s - 2 | + C ( p ) 2 ln | x - 1 | + tan - 1 ( x ) + C 2. Let f ( x ) = x 1 - ln( x + 1) . (a) Determine the domain of f ( x ). (b) Find the derivative of f ( x ).
(b) Use the quotient (or product rule).