Unit 9 pt2 test

Question 1

a. Integration by parts
b. derivative of u/v

Answer 1

a. int udv=uv-int vdu
b. (u’v-uv’)/v^2

Question 2

a. int lnxdx =
b. int tanxdx =
c. int secxdx =
d. int cotx dx
e. int cscxdx =

Answer 2

a. xlnx -x + c
b. ln|secx| + C
c. ln|secx+tanx| + C
d. ln |sinx| + C
e. ln |cscx - cotx| + C

Question 3

a. cos^2x =
b. sin^2x =

Answer 3

a. 1/2(1+cos2x)
b. 1/2(1-cos2x)

Question 4

Derivative of:
a. sin^-1x =
b. tan^-1x =
c. sec^-1 =

Answer 4

a. 1/ sq1-x^2
b. 1/1+x^2
c. 1/ |x|sq x^2 -1

Question 5

Integral of:
a. int sin^-1 =
b. int cos^-1 =
c. int tan^-1 =

Answer 5

a. xsin^-1x + sq1-x^2 + c
b. xcos^-1x - sq1-x^2 + c
c. xtan^-1x - lnsqx^2+1 + c

Question 6

Integral of:
a. int cot^-1 =
b. int sec^-1 =
c. int csc^-1 =

Answer 6

a.. xcot^-1x + lnsqx^2+1 + c
b. xsec^-1x - sgnln|x+ sqx^2 -1| + c
c. xcsc^-1x + sgnxln|x + sqx^2-1| + c

Question 7

a. sin2x
b. tan^2x

Answer 7

a. 2sinxcosx
b. 1-cos2x/1+cos2x