MATH 2202 –Quiz 1 (Version 2) Solution
January 16, 2008
NAME_______________________________________
1. Use a substitution to evaluate the inde…nite integral
Zsin (2x)dx.
2. Use di¤erentiation to check whether or not the answer you obtained
in part 1 is correct. Have you found that your answer is correct or
incorrect?
You must show your procedures in order to receive any credit. You will
not receive credit if you just write down an answer without showing how that
answer was obtained.
Solution
1. To evaluate this inde…nite integral, we use the substitution
u= 2x
du = 2 dx.
We then evaluate the integral as follows:
Zsin (2x)dx =1
2Zsin (u)du =1
2(cos (u)) + C=1
2cos (2x) + C.
2. Show the check of your answer here. Do you …nd that your answer is
correct or incorrect? (Please answer this in a complete sentence.)
d
dx 1
2cos (2x)=1
2(sin (2x)) (2) = sin (2x)
shows that our answer is correct.
1