Integration

Question 1

What is the trapezium rule?

Answer 1

∫ y dx = 1/2 h [( first + last ) + 2( sum of terms in between)]

Question 2

Where do you use reverse chain rule?

Answer 2

When the original function could have been differentiated by chain rule to get this. Eg. F ‘(g (x)) ~> g ‘(x) f ‘(g(x))
(So in diff X out diff (orig. in))

Question 3

How do you integrate by reverse chain rule?

Answer 3

Integrate outside the brackets, integrate the whole bracket as an x^a term and then divide all by inside the bracket differentiated

So, int outside • n+1( og inside) • 1/ diff inside

Question 4

∫ ax^n integrates to

Answer 4

a/(n+1) • x^(n+1) + c

Question 5

e^x integrates to

Answer 5

e^x + c

Question 6

1/x integrates to

Answer 6

Ln |x| + c

Question 7

Cos kx integrates to

Answer 7

1/k Sin kx + c

Question 8

Sin kx integrates to

Answer 8

-1/k Cos kx + c

Question 9

Sec^2 x integrates to

Answer 9

Tan x + c

Question 10

Sec x Tan x integrates to

Answer 10

Sec x + c

Question 11

Cosec^2 x integrates to

Answer 11

• Cot x + c