What is f(x) = int 3x dx if f(2) = 7 ?

2 Answers
Mar 21, 2017

The answer is f(x)=3/2x^2+1

Explanation:

We need

intx^ndx=x^(n+1)/(n+1)+C (n!=-1)

So,

f(x)=int3xdx=3/2x^2+C

f(2)=6+C=7

:. C=7-6=1

f(x)=3/2x^2+1

Mar 21, 2017

f(x) = (3x^2)/2+1

Explanation:

Evaluate the indefinite integral:

f(x) = int 3xdx = (3x^2)/2 +C

Use the initial condition to determine C:

f(2) = 12/2+C = 7

so:

C = 7-6 = 1

and:

f(x) = (3x^2)/2+1