10 - MoreSubst

10 - MoreSubst - Substitution cont'd So far: 1. Use basic...

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Unformatted text preview: Substitution cont'd So far: 1. Use basic forms 2. Simplify if possible (multiply out or break apart) 3. Use u-substitution 4. Use linear substitution 1+ x dx Ex. 1 + x 2 Ex. x2 dx 1- x Do: Find x x + 1 dx Definite integrals Ex. 4 0 tan 3 d 2 cos x2 dx Ex. 0 1 + x 3 1 Ex. Let B be the upper limit of the definite integral obtained by substitution: 3 0 (2x - 3)h(x - 3x + 7)dx = 2 B A h(u)du Which of the following holds? a. 9 < B b. 6 < B 9 c. 3 < B 6 d. 0 < B 3 e. B 0 Ex. y ( ln y + 1) 1 2 + 9 dy Ex. 2 - 2 cos y dy sin y + 2 Symmetry: Let f be continuous on [-a, a] a. If f is even, ( f (-x) = a 0 f (x)) , then a -a f (x) dx = 2 f (x) dx . b. . If f is odd, Do: 1. ( f (-x) = - f (x)) , then a -a f (x) dx = 0 . 4 0 sin x dx cos x 9 2. 1 (1 + x ) x 0 dx 3. 1 1 2 1 x 1 + 2 1 1 + x 4 2 dx 3 4. 0 1 dx 2 x + 2x + 1 Completing the square Ex. x2 + x + 3 Ex. 3 - x2 + x Ex. 3x 2 + x + 3 Ex. If there is a substitution y(x) that gives 1 -1 2x 2 - 7x + 5 dx = A tan ( y ) , find A. Ex. 2 0 1 -1 T dx = A tan y R 2 5x - 2x + 3 Find T. Do: Ex. If there is a substitution y(x) that gives T 1 -1 -3 2x 2 - 6x + 5 dx = A tan ( y ) R , find A, y and T. 4 ...
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