by Guest » Sat Feb 27, 2021 10:28 pm
One reason we ask people to first try problems themselves then show their work is that it helps us see what you DO know and CAN do!
If you know basic integration then you should know that [tex]\int ax^n dx= \frac{a}{n+1}x^{n+1}+ C[/tex].
If you do not know that do you at least know that the derivative of [tex]ax^n[/tex] is [tex]anx^{n-1}[/tex] and that "integration" is the inverse of "differentiation"? In order that the derivative be [tex]x^{3/2}[/tex] we must have [tex]anx^{n-1}= x^{3/2}[/tex] we must have an= 1 and n-1= 3/2. If n-1= 3/2 then n= 3/2+ 1= 5/2 and a= 2/5 so
[tex]ax^n= (2/5)x^{5/2}[/tex]. (Plus any constant since the derivative of a constant is 0.)