ch11 integration

Question 1

What is the general form when integrating f’(ax+b)

Answer 1

Divide by the derivative

1/a f(ax+b).

Question 2

How to deal with integrating (1/3x+2)

Answer 2

firstly ln(3x+2) then divide by the derivative of 3x+2 so 1/3ln(3x+2)

Question 3

How to deal with integrating (2x+3)^4?

Answer 3

Raise the power by 1, then divide by the raised power and the derivative of the bracket.

Question 4

How to apply the reverse chain rule?

Answer 4

-Raise the power of the bracket by 1 then divide by both the power and the derivative of the bracket.

Question 5

How to Integrate (Sin^2x)?

Answer 5

Use the cos double angle identity and this will give you something that can be integrated.
1/2-1/2cos2x

Question 6

How to integrate (Cos^2x)?

Answer 6

Use the cos double angle identity and this will give something that can be integrated.
1/2 + 1/2cos^2x

Question 7

What to integrate when there is a bracket squared?

Answer 7

• Expand the bracket
• Use the identity to sub in something that can be integrated
• Integrate.

Question 8

How to integrate when you have 1/ sin^2x Cos^2x

Answer 8

• Make it 1/ (sinxcosx)^2
• Use double angle formula to sub in for sinxcosx
• Then integrate.

Question 9

If a question asks you to do integration by substitution with appropriate substitution what do you do?

Answer 9

-Go to further maths AS page and see which substitution will resemble the one you must do the most.
Eg if it is 1/1+x^2 you know it must be x=tantheeta

Question 10

How to do trapezium rule?

Answer 10

Establish height and number of strips.

-Then sub into formula in formula which is in formula booklet.

Question 11

How do you know the height in the trapezium rule?

What to not get confused with strips?

Answer 11

Upper limit - lower limit / number of strips.

-One less than columns.