Integration

Question 1

e^f(x)

Answer 1

(1/f’(x))e^f(x)

Question 2

1/x

Answer 2

ln(x)

Question 3

sin(x)

Answer 3

-(1/f’(x))cosf(x)

Question 4

sec^2f(x)

Answer 4

(1/f’(x))tanf(x)

Question 5

cosecf(x)cotf(x)

Answer 5

-(1/f’(x))cosec^2f(x)

Question 6

cosec^2f(x)

Answer 6

-(1/f’(x))cotf(x)

Question 7

secf(x)

Answer 7

(1/f’(x)) ln(secf(x) + tanf(x))

Question 8

cosf(x)

Answer 8

(1/f’(x))sinf(x)

Question 9

secf(x)tanf(x)

Answer 9

(1/f’(x))secf(x)

Question 10

cosf(x)

Answer 10

(1/f’(x))sin(x)

Question 11

tanf(x)

Answer 11

(1/f’(x)) ln(secf(x))

Question 12

what do you use to integrate 1/f(x)^u

Answer 12

Bring power up so is negative and then use chain rule

Question 13

a^x

Answer 13

a^x/ln(a)

Question 14

cos^2(x)

Answer 14

0.5(0.5sin(2x) + x)

Question 15

sin^2(x)

Answer 15

0.5(x - 0.5sin(2x)

Question 16

cot^2(x)

Answer 16

-cot(x) - x + c

Question 17

tan^2(x)

Answer 17

tan(x) - x + c

Question 18

Integration by parts

Answer 18

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

Question 19

How can cos^2(x) and sin^2(x) be rewritten in proving questions

Answer 19

Cos^2(x)= 0.5+0.5cos(2x)
Sin^2(x)= 0.5-0.5cos(2x)

Question 20

Always remember +c if there is no bounds

Answer 20

Always remember +c if there is no bounds

Question 21

remember when 1/linear you must use logs to integrate

Answer 21

example 10(2x-1)^-1 goes to 5ln(2x-1)

Question 22

Trapezium rule

Answer 22

{= integral with upper bound b and lower bound a

{ydx ~ 0.5h(y0+2(y1+y2+…yn-1+)+yn)