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Material Type: Notes; Class: Calculus II; Subject: Mathematics; University: Pellissippi State Technical Community College; Term: Unknown 2000;
Typology: Study notes
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Integration Using Tables ~ p. 1 J. Ahrens 2000-
Objective: Evaluate integrals using tables of integrals
It is frequently necessary to use substitution along with integral tables.
It may be necessary to use a formula more than once or to use two or more formulas.
Evaluate
2 2
0 2
x 12 dx
x 4
1
2 2
du 1 u tan C a u a^ a
− = +
2
2 2
x 12 8 1 x 4 x 4
2 2
0 2
x 12 dx
x 4
2
0 2
1 dx
x 4
2 1 1
0
1 x x 8 tan 2 4 tan 1 2 2 2
π
Evaluate
2
2
x dx
5 −4x
2 2 2 2 1
2 2
u u a u du a u sin C 2 2 a a u
u du 2dx and x 2
2
2
2 2
u
x (^1 ) dx du 2 5 4x 5 u
2 a = 5
2
2
2 2
u
1 2 1 u du du 2 8 5 u 5 u
1 u 2 5 1 u 5 u sin C (^8 2 2 )
Integration Using Tables ~ p. 2 J. Ahrens 2000-
Evaluate
3 x sin x dx
3 3 2 x sin x dx = − x cos x + 3 x cos x dx
2 2 x cos x dx = x sin x − 2 x sin x dx
3 x sin x dx
3 2 = − x cos x + 3x sin x − 6 sin x + 6xcosx +C