Integration P2

Question 1

what is the integration of cosecx cotx

Answer 1

-cosecx + c

Question 2

what is the integration of secx tanx

Answer 2

secx + c

Question 3

what is the integration of cosec^2x

Answer 3

-cotx + c

Question 4

what is the integration of cosec(ax+b) cot(ax+b)

Answer 4

-1/a cosec(ax+b) + c

Question 5

what is the integration of sec(ax+b) tan(ax+b)

Answer 5

1/a sec(ax+b) + c

Question 6

what is the integration of cosec^2(ax+b)

Answer 6

-1/a cot(ax+b) + c

Question 7

what is the double angle formula for sin2A

Answer 7

sin2A = 2(sinA cosA)

Question 8

what is the double angle formula for cos2A

Answer 8

cos2A = cos^2A - sin^2A

Question 9

what is the double angle formula for tan2A

Answer 9

tan2A = (2tanA) / (1 - tan^2A)

Question 10

just as a quick reminder, what do i mean by sin^2A

Answer 10

(sinA)^2

Question 11

what does the integration of f’(x) / f(x) equal

Answer 11

ln(|f(x)| + c)

Question 12

what does ln(|f(x)| + c) equal when a k rather than a c where the c is basically the k

Answer 12

• ln|f(x)| + lnk

- ln(k * |f(x)|)

Question 13

what is the integration of tan kx

Answer 13

1/k ln|sec kx| + c

Question 14

what is the integration of cosecx

Answer 14

-ln[cosecx + cotx] + c

Question 15

what is the integration of secx

Answer 15

ln[secx + tanx] + c

Question 16

what is the integration of cotx

Answer 16

ln[sinx] + c

Question 17

what would the integration of any of these (kx) functions be

Answer 17

1/k ln{ whatever this is (kx)] + c

Question 18

What is the formula for parametric integration

Answer 18

Integration of y (dx) = integration of y * dx/dt (dt)

Question 19

what is the integration of f’(x) / f(x)

Answer 19

• ln |f(x) + c|

- which = ln |k * f(x)|

Question 20

what is the formula for integration by parts

Answer 20

int (uv’) = uv - in (vu’)

Question 21

how do you find f(u) from the int (du/dx f’(u))

Answer 21

du/dx * int(f’(u)) = f(u) + c

Question 22

what is the equation for int(y) dx with parametric equations

Answer 22

• int(y) dx = int(y * dx/dt) dt
• your y and dx/dt are in terms of y so multiply them and int with respects to t
• you will need to convert limits in terms of t if needed

Question 23

what is the small angle approximation of sin0

Answer 23

sin0 = 0

Question 24

what is the small angle approximation of cos0

Answer 24

cos0 = 1 - (1/2 0^2)

Question 25

what is the small angle approximation of tan0

Answer 25

tan0 = 0