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quiz1ws2009 - Z sin x cos x dx = 1 2 sin 2 x C =-1 2 cos 2...

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Quiz 1 Instructor: Stephan Spencer Section 14 22 January, 2009 Student Name: 1. Solve the Following Integrals using rules or substitutions: a) Z cos 3 x dx b) Z x 3 (2 + x 4 ) 5 dx c) Z x 2 p x 3 + 1 dx d) Z cos 3 θ sin θ dx e) Z 1 x 2 sec 2 1 x dx f) Z cos t t dx g) Z x ( x 2 + 1) 2 dx h) Z (3 t + 2) 2 . 4 dt i) Z ( x + 1) p 2 x + x 2 dx j) Z a + bx 2 3 ax + bx 3 dx k) Z x 2 1 - x dx l) Z a 0 x p x 2 + a 2 dx m) Z (1 + 1 u ) - 3 ( 1 u 2 ) du n) Z cos (4 x - 2) sin (4 x - 2) dx o) Z ( x 2 + 1) 3 dx p) Z 2 a a 2 x - a dx 1
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2. Show, by evaluating in three different ways, that
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Unformatted text preview: Z sin x cos x dx = 1 2 sin 2 x + C =-1 2 cos 2 x + D =-1 4 cos 2 x + E 3. Verify the following formulas a) Z √ x 2-a 2 x 4 dx = p ( x 2-a 2 ) 3 3 a 2 x 3 + C b) Z 1 x 2 √ x 2-a 2 dx = √ x 2-a 2 a 2 x + C 2...
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quiz1ws2009 - Z sin x cos x dx = 1 2 sin 2 x C =-1 2 cos 2...

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