What is f(x) = int xsqrt(3x) dx if f(3) = 0 ?

1 Answer
May 7, 2016

=>f(x) = (2sqrt(3))/5x^(5/2) -54/5

Explanation:

f(x) = int xsqrt(3x) dx
=>f(x) = sqrt(3)int xsqrt(x) dx
=>f(x) = sqrt(3)int x^(3/2) dx
=>f(x) = sqrt(3)x^(3/2+1)/(3/2+1) +c [where c = Integration constant]

=>f(x) = (2sqrt(3))/5x^(5/2) +c.....(1)

Again given condition is f(3)=0
So
=>f(3) = (2sqrt(3))/5xx3^(5/2) +c
=>0= 2/5xx3^(5/2+1/2) +c
=>0= 2/5xx3^3 +c
=>0= 54/5 +c
=>c= -54/5
Hence we have , substituting the value of c in eq(1)

=>f(x) = (2sqrt(3))/5x^(5/2) -54/5