integration

Question 1

possible questions

Answer 1

• integration
• definite integrals
• area under a curve
• area between two curves
• differential equations
• integrating sin and cos
• integrating composite functions

Question 2

area under a curve process

remember dx and +c

Answer 2

• integrate and place a and b at end of bracket
• sub a and b into x
• simplify
• answer in units²

Question 3

area between two curves process

remember dx and +c

Answer 3

• calculate a and b by equalling two equations and factorising
• set up integral with a and b (upper-lower)
• sub a and b into x
• simplify
• answer in units²

Question 4

differential equation process

remember dx and +c

Answer 4

• place integral sign infront of dy/dx and equation
• integrate
• sub x and y into equation
• simplify and equal to c
• sub c into simplified integrated equation

Question 5

integrating composite functions steps

remember dx and +c

Answer 5

• +1 to power and divide by (new power x diff of middle)
• simplify with +c

example:

• ∫(3x-2)⁵ dx
• = (3x-2)⁶/ 6x3 +c
• = (3x-2)⁶/18 +c

Question 6

integrating sin and cos steps

remember dx and +c

Answer 6

Q: ∫4sin(2x-1) dx

• = -4½ cos(2x-1) +c
• = -2 cos(2x-1) +c
• (may need to sub in integrals here)