Pure Year 2 Unit 11

Question 1

Integration of X^n

Answer 1

(x^(n+1)) / (n+1)

Question 2

Integration of e^x

Answer 2

e^x

Question 3

Integration of 1/x

Answer 3

ln(x)

Question 4

Integration of cos(x)

Answer 4

sin(x)

Question 5

Integration of sin(x)

Answer 5

-cos(x)

Question 6

Integration of sec^2(x)

Answer 6

tan(x)

Question 7

Integration of cosec(x)cot(x)

Answer 7

-cosec(x)

Question 8

Integration of cosec^2(x)

Answer 8

-cot(x)

Question 9

Integration of sec(x)tan(x)

Answer 9

sec(x)

Question 10

Integration f’(ax+b)

Answer 10

(1/a) * f(ax+b)

Question 11

Formula for integration by parts

Answer 11

Integration of u * dv/dx = uv - integration of v * du/dx

Question 12

Trapezium rule formula

Answer 12

Integration of y between a and b = (h/2)(y0 + 2(y1 + y2 + y3 …. + Yn-1 ) + yn)

Question 13

When dy/dx = f(x)g(y), how can this be rewritten?

Answer 13

Integration 1/g(y) = Integration of f(x)

Question 14

Integration of the limit of a sum for the integration of f(x) between a and b

Answer 14

limit of dx –> 0 for sigma f(x) when x = a and b on the top