A* Finish With A Bang

Question 1

Integration of ln(x)

Answer 1

Use substitution

-> 1•ln(x)

Question 2

Parametric to Cartesian involving trig

Answer 2

Use identities
•sin ² x + cos ² x = 1

• 1 + cot ² x = cosec ² x
• tan ² x + 1 = sec ² x

Question 3

What to do if stationary point is y=x during implicit differentiation

Answer 3

Put y=x into undifferentiated equation and find coordinates of stationary points

Question 4

Integrate 2 ˣ

Answer 4

2 ˣ
——— + C
ln(2)

Question 5

Differentiate 2 ˣ

Answer 5

2 ˣ•ln(2)

Question 6

Integrate sin²x

Answer 6

• use cos2x = 1-2sin ² x
• rearrange
• integrate

Question 7

Integrate cos²x

Answer 7

• use cos2x = 2cos ² x-1
• rearrange
• integrate

Question 8

Integrate cot²x

Answer 8

• use 1 + cot²x = cosec²x
• rearrange
• integrate

Question 9

3 standard patterns

Answer 9

For e
• f’(x)eᶠ⁽ˣ⁾ -> let y= eᶠ⁽ˣ⁾

For ln
• f’(x)/f(x) -> let y= ln(f(x))

For non liner powers
• f’(x)[f(x)] ⁿ -> let y= [f(x)] ⁿ⁺¹

Question 10

Area of a parallelogram

Answer 10

Area = absinC

Twice area of triangle