differentiation and integration

Question 1

what is partial differentiation ?

Answer 1

when f(x,y) and you take a derivative of only one of the variables

df/dx or df/dy

Question 2

what are these integrals ?

a. k
b. x^n n=/1
c. 1/x
d. e^ax
e. g’(x)/g(x)

Answer 2

a. kx + c
b. x^n+1 / n+1 + c
c. ln|x| + c
d. e^ax/a + c
e. ln|g(x)| + c

Question 3

name these rules of integration ?

a. s(f(x) + g(x)) =
b. if k is constant
s(kf(x)) =

Answer 3

a. s(f(x)) + s(g(x))

b. k . s(f(x))

Question 4

how do you calculate area A ?when A is under f(x) from x=a to x=b

Answer 4

a
A = sb(f(x))dx

[ sf(x)]ab

(sf(a)) - (sf(b))

Question 5

how do you integrate by parts?

Answer 5

when the equation has two functions :

turn the function into u.dv/dx

chose the u based on (ILATE)

I = uv - s (v.du/dx) dx

Question 6

how do you integrate by substitution ?

Answer 6

chose something to sub out and re arrange with the differentiation and then at the end re sub the original in