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Published byAvis McDaniel Modified over 8 years ago
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Clicker Question 1 According to the FTC Part 1, what is an antiderivative of f (x ) = sin(x 2 ) ? A. B. C. –cos(x 2 ) D. –cos(x 3 /3) E. -2x cos(x 2 )
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Antiderivatives: Trying to Reverse the Chain Rule (4/18/12) Any ideas about x 2 (x 3 + 4) 5 dx ?? How about x e x^2 dx ? Try ln(x)/x dx But we’ve been lucky! Try sin(x 2 ) dx
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What the 3 Examples Above Had in Common: There was a chunk. There was also a multiplier which was the derivative of the chunk except for possibly a missing constant multiplier. This should allow us to see what an antiderivative is, making the appropriate adjustment for the missing constant multiplier.
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Some More Examples x 2 sin(x 3 + 2) dx (4x + 5) 100 dx sin(t ) cos(t ) dt
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Clicker Question 2 What is x 3 (x 4 – 3) 5 dx ? A. (1/6)(x 4 – 3) 6 + C B. (1/24)x 4 (x 4 – 3) 6 + C C. (2/3)(x 4 – 3) 6 + C D. (1/24)(x 4 – 3) 6 + C E. (2/3)x 4 (x 4 – 3) 6 + C
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Clicker Question 3 What is ((ln(x )) 2 / x ) dx ? A. (ln(x )) 3 / (3x ) + C B. (ln(x )) 3 / 3 + C C. 2(ln(x )) 3 / (3x 2 ) + C D. 3(ln(x )) 3 / (2x 2 ) + C E. (ln(x )) 3 / 6 + C
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Assignment for Friday On pages 413-14 of our text, do Exercises 7, 9, 11, 13, 15, 17, 23, 25, 29, 31 and 33.
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