Yr 2 - Integration (Chapter 11)

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 sinx

Answer 5

, - cosx + c

Question 6

integrate sec^2 x

Answer 6

tan x + c

Question 7

integrate cosec x cot x

Answer 7

, - cosec x + c

Question 8

integrate cosec^2 x

Answer 8

, - cot x + c

Question 9

integrate sec x tan x

Answer 9

sec x + c

Question 10

integrate f’(ax + b)

Answer 10

1/a f(ax + b) + c

Question 11

how to integrate k( f’(x) / f(x) )

Answer 11

try ln |f(x) | and differentiate and adjust for constants

Question 12

how to integrate k[ f’(x)][ f(x)^n]

Answer 12

try f(x)^(n+1) and differentiate, then adjust for any constant

Question 13

What is the method for integrating by parts

Answer 13

integral [u(dv/dx) dx ] = uv - integral [v(du/dx) dx]

Question 14

how to find area bound between two curves, between x = a and x = b

Answer 14

integral b->a [f(x) - g(x) ] dx

Question 15

What is the formula for trapezium rule for integral b->a [y dx]

Answer 15

1/2 h( y0 + 2( y1 + y2 … + yn − 1) + yn)

Question 16

if dy/dx = f(x) g(y) how to rewrite as an differential equation

Answer 16

integral [1/g(y) dy] = integral [f(x) dx]