Integration

Question 1

Trapezium Rule

Answer 1

1/2 h(y0 + yn + 2(y1 + … + yn-1))

Question 2

∫ cos x dx

Answer 2

∫ cos x dx = sin x + c

Question 3

∫ e^kx dx

Answer 3

∫ e^kx dx = 1/k e^kx + c

Question 4

∫ e^(kx + b) dx

Answer 4

∫ e^(kx + b) dx = 1/k e^(kx + b) + c

Question 5

∫ tan x dx

Answer 5

∫ tan x dx = ln |sec(x)| + c

Question 6

∫ sin x dx

Answer 6

∫ sin x dx = -cos x + c

Question 7

∫ f’(x) / f (x) dx

Answer 7

∫ f’(x) / f (x) dx = ln |f(x)| + c

Question 8

Integration by Parts

Answer 8

∫ u dv/dx dx = uv - ∫ (u du/dx) dx

Make u = ln x or u = the power of x

Question 9

∫ a^x dx

Answer 9

(ln a) (a^x)

Question 10

∫ ln x

Answer 10

(xln x) - x