Final Exam Term 121 Term 112 Improper Integral

Final Exam Term 121 Term 112 Improper Integral and Ch 10 16 16 Others 12 12 Remark: (24) 1) Chapter 10 Term 121 Term 112 Others (Techniques of Integrations) 8 8 Others-Others 4 4 2) Improper Integral 3) Techniques of Integration

TECHNIQUES OF INTEGRATION

TECHNIQUES OF INTEGRATION

Final 112 Final 121 Final 102

By Parts Partial Fraction Long Divison factor denom express coverup at least one odd Keep one with dx Trig Subs All even Use half angle

INTEGRATION BY PARTS Most of the time ln(x) is easier by parts Integration by Parts Repeated Applications Term 0 (diff) tabular integration Back to original

Final 112 Final 121 Final 102

TERM-112

TERM-121

Final 121 Final 112 Final 102

Final 112 Final 121 Final 102

Fundamental Theorem Of Calculus

Fundamental Theorem Of Calculus

TERM-121 Differentiate Approximate

Numerical Integration: Simpson's rule

Arclength Surface Area about the x-axis about the y-axis

Surface Area about the x-axis about the y-axis

DONOT Confuse: Area of the region bounded by the curve Surface Area generated by

1 SKIM and Classify 7 DONOT GIVE UP (RELAX use 3 Hours) (Easy, M, Hard) 2 Start by Easy 3 No bubble , just circle 4 Next M then H 5 6 Use answers to Question At end, revisit and check (use different method) 8 Guess (be smart) 1)Eliminate 2)Look for pattern 3)Approximate 4)Subsitute by values 5)Count and be consistent (b) 9 10 Last 15 min bubble Say and pray