Calculus + Antiderivative

Question

Consider the function f(x)=3/x² - 3/x⁶

 

Let F(x) be the antiderivative of f(x) with F(1)=0

Answer 1

F(1)=0

F'(x)=f(x)=3/x² -3/x⁶

I am assuming you want to find F(x)

 

The anti derivative of an expression in the form kx^a  is found by (k/(a+1))x^a+1 +c

 

You may find it easier to follow if you rewrite f(x)=3x^-2 -3x^-6

Thus we get F(x)=-3x^-1 +3/5 x^-5 +c

Then F(1)=-3/1 + 3/5 + c = 0  so that c = 12/5

 

Finally F(x) = 3/(5x⁵) - 3/x + 12/5