What is f(x) = int xsqrt(x^2-2) dx if f(3) = 3 ?

1 Answer
Apr 11, 2016

f(x)=1/3 (x^2-2)^(3/2) +3-(7sqrt7)/3

Explanation:

f(x)=intxsqrt(x^2-2)dx=intx(x^2-2)^(1/2)dx

Note that the x outside of the square root is part of the derivative of the inside so we can just integrate (x^2-2)^(1/2)

f(x)=intx(x^2-2)^(1/2)dx = 2/3 (x^2-2)^(3/2)*1/2-> since the 2 from the derivative of the inside is missing.

f(x)=1/3 (x^2-2)^(3/2) +C
f(3)=1/3 (9-2)^(3/2)+C=3
(7sqrt7)/3 +C =3
C=3-(7sqrt7)/3
f(x)=1/3 (x^2-2)^(3/2) +3-(7sqrt7)/3