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 )

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

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.

Some More Examples  x 2 sin(x 3 + 2) dx  (4x + 5) 100 dx  sin(t )  cos(t ) dt

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

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

Assignment for Friday On pages of our text, do Exercises 7, 9, 11, 13, 15, 17, 23, 25, 29, 31 and 33.