Week 7 Integration 2

Question 1

what is the integration by parts general formula

Answer 1

uv = ∫uv’ + ∫vu’

Question 2

what is the general line integral equation

Answer 2

b
∫ sqrt[ 1 + (dy/dx)^2 ] dx
a

Question 3

what is the general formula for finding the area of a polar coordinate system curve

Answer 3

θ’
∫1/2 r^2 dθ
0

Question 4

what is the idea of integration by differentiation

Answer 4

take the original integral and by inspection find another integral which is simpler than the original and when differentiated wrt a parameter gives the original integral