Improper Integrals and IMF

Question 1

What are the four ways to solve integral and intermediate problems?

Answer 1

1) L’Hopitals
2) U-Substitution and Factoring
3) Logarithmic Functions
4) Straight Plug In

Question 2

Where do discontinuities lie?

Answer 2

Lower and upper limits, as well as inside the function

Question 3

e^ln(y)

Answer 3

y

Question 4

e^0

Answer 4

1

Question 5

ln(1)

Answer 5

0

Question 6

1/0

Answer 6

+infinity

Question 7

1/infinity

Answer 7

0

Question 8

Do you KNOW u substitution?
du and how it relates to dx?

Answer 8

Derive u to get du, then make du=u’dx
du/u’=dx
Plug that in for dx

Question 9

Integral of x^n

Answer 9

(x^n+1)/n+1

Question 10

(d/dx)tanx

Answer 10

(secx)^2

Question 11

(d/dx)-cotx

Answer 11

(cosecx)^2

Question 12

(d/dx)secx

Answer 12

secxtanx

Question 13

(d/dx)-cosecx

Answer 13

cosecxcotx

Question 14

(d/dx)e^x

Answer 14

e^x

Question 15

(d/dx)log|x|

Answer 15

1/x

Question 16

(d/dx)ln(x)

Answer 16

1/x

Question 17

(d/dx)[(a^x)/(loga)]

Answer 17

a^x

Question 18

(d/dx)[sinx]^-1

(d/dx)[cosx]^-1

Answer 18

1/(1-x^2)sqrt
Same but negative in front

Question 19

(d/dx)[tan]^-1

(d/dx)[cot]^-1

Answer 19

1/1+x^2
Same but negative in front

Question 20

(d/dx)[sec]^-1

(d/dx)[cosec]^-1

Answer 20

1/|x|(x^2-1)(sqrt)
Negative in front (c’s mean negative!)