C4- Integration

Question 1

∫(1/x)dx

Answer 1

ln|x| + c

Question 2

∫sinx dx

Answer 2

-cosx +c

Question 3

∫cosx dx

Answer 3

sinx +c

Question 4

∫tanx dx

Answer 4

ln|secx| +c

Question 5

∫cotx dx

Answer 5

ln|sinx| +c

Question 6

∫secx dx

Answer 6

ln|secx + tanx| +c

Question 7

∫cosecx dx

Answer 7

-ln|cosecx + cotx| +c

Question 8

∫sec^2(x) dx

Answer 8

tanx +c

Question 9

∫-(cosecx)(cotx) dx

Answer 9

cosecx +c

Question 10

∫(secx)(tanx) dx

Answer 10

secx +c

Question 11

∫-cosec^2(x) dx

Answer 11

cotx +c

Question 12

∫(f’(x))/(f(x)) dx

Answer 12

ln|f(x)| +c

Question 13

∫f(x)[f(x)]^n dx

Answer 13

[1/n+1][f(x)]^(n+1)

Question 14

What is the formula for integrating by parts?

Answer 14

∫u(dv/dx) dx = uv - ∫v(du/dx) dx

Question 15

What is the formula for the volume of revolution around the x-axis between x=a and x=b?

Answer 15

π∫ (y^2 dx)

Question 16

How do you separate the variables of: dy/dx=[f(x)][g(y)]?

Answer 16

∫(1/g(y)) dy = ∫f(x) dx

Question 17

What is the trapezium rule?

Answer 17

∫y dx= (1/2)(h)[y0 + yn + 2(y1+y2+y3+…+yn-1)]

where h=(b-a)/n

Question 18

∫1/(ax+b) dx

Answer 18

(1/a)(ln|ax+b|) +c

Question 19

∫cos(ax+b) dx

Answer 19

(1/a)(sin(ax+b)) +c

Question 20

∫sin(ax+b) dx

Answer 20

-(1/a)(cos(ax+b)) +c

Question 21

∫sec^2(ax+b) dx

Answer 21

(1/a)(tan(ax+b)) +c

Question 22

∫cosec(ax+b)cot(ax+b) dx

Answer 22

-(1/a)(cosec(ax+b)) +c

Question 23

∫cosec^2(ax+b) dx

Answer 23

-(1/a)(cot(ax+b)) +c

Question 24

∫sec(ax+b)tan(ax+b) dx

Answer 24

(1/a)(sec(ax+b)) +c