Integration

Question 1

Integrate x^n

Answer 1

( x^(n+1)/ n+1 ) + c

Question 2

Integrate e^x

Answer 2

e^x + c

Question 3

Integrate 1/x

Answer 3

ln |x| + c

Question 4

Integrate cosx

Answer 4

sinx + c

Question 5

Integrate f(ax + b)

Answer 5

= (1/a) f (ax + b) + C

Question 6

Integrate sin3xcos3x

Answer 6

Double angle formula
To get 0.5sin6x - as we can integrate this from our knowledge
= ( -cos6x /12 ) + c

Question 7

Integrate tan^2 x

Answer 7

Use tan^2x + 1 = sec^2x
= tanx - x + c

Question 8

What are the 3 steps using parametric equations to find area under curve?

Answer 8

1. Find dx/dt (∫ y dx = ∫ y (dx/dt) dt )
2. Change range - x terms to in terms of t
3. Integrate (in terms of t)

Question 9

Integrate lnx

Answer 9

xlnx - x + c
LEARN
Using integrate by parts, u=lnx , dv = 1

Question 10

How to integrate by parts

Answer 10

uv - ∫v(du/dx) + c
x^n term is always u, except ln|x|