What is f(x) = int xsqrt(3x) dxf(x)=∫x√3xdx if f(3) = 0 f(3)=0?

1 Answer
P dilip_k
May 7, 2016

=>f(x) = (2sqrt(3))/5x^(5/2) -54/5⇒f(x)=2√35x52−545

Explanation:

f(x) = int xsqrt(3x) dxf(x)=∫x√3xdx
=>f(x) = sqrt(3)int xsqrt(x) dx⇒f(x)=√3∫x√xdx
=>f(x) = sqrt(3)int x^(3/2) dx⇒f(x)=√3∫x32dx
=>f(x) = sqrt(3)x^(3/2+1)/(3/2+1) +c⇒f(x)=√3x32+132+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

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