Math Practice on Tuesday: 190312 Tue – About volume of rotating body around x axis


y=sqr(x+1)-1, x axis, line x=3, surrounded area volume.

V=S[a-b](integral)  S(x) dx  (condition a>b)


But I rested really long time, so I missed

S(Integral) x^α+1 dx = (1/ α+1)x^ α+1 + C


I have to master “various kind of functions of indefinite integral”

This case

S(integral) f(ax+b)dx = 1/a F(ax+b) + C

Proof of elemental formulae …

Calculate like a machine …

This is from Japanese high school book for University Admission,

“Chart (White) 3+C 2008” P225, Standard Example 146.