What is f(x) = int sqrt(x+3) dx if f(1)=7 ? Calculus Techniques of Integration Evaluating the Constant of Integration 1 Answer sjc May 26, 2018 f(x)=2/3(1+3)^(3/2)+5/3 Explanation: f(x)=intsqrt(x+3)dx f(x)=int(x+3)^(1/2)dx now d/(dx)(x+3)^(3/2)=3/2(x+3)^(1/2) f(x)=int(x+3)^(1/2)dx=2/3(x+3)^(3/2)+c now f(1)=7 :.2/3(1+3)^(3/2)+c=7 2/3xx8+c=7 16/3+c=7 =>c=7-16/3 c=5/3 :.f(x)=2/3(1+3)^(3/2)+5/3 Answer link Related questions How do you find the constant of integration for intf'(x)dx if f(2)=1? What is a line integral? What is f(x) = int x^3-x if f(2)=4 ? What is f(x) = int x^2+x-3 if f(2)=3 ? What is f(x) = int xe^x if f(2)=3 ? What is f(x) = int x - 3 if f(2)=3 ? What is f(x) = int x^2 - 3x if f(2)=1 ? What is f(x) = int 1/x if f(2)=1 ? What is f(x) = int 1/(x+3) if f(2)=1 ? What is f(x) = int 1/(x^2+3) if f(2)=1 ? See all questions in Evaluating the Constant of Integration Impact of this question 1950 views around the world You can reuse this answer Creative Commons License