What is f(x) = int sqrt(x+3) dx if f(1)=7 ?

1 Answer
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