# int_a^b(x^2)dx = (b^3 - a^3)/3 Prove that

sciencesolve | Certified Educator

You need to evaluate the definite integral, such that:

int_a^b f(x) dx = F(b) - F(a)

int_a^b x^2 dx = (x^3)/3|_a^b

int_a^b x^2 dx = (b^3)/3 - (a^3)/3

int_a^b x^2 dx = (b^3 - a^3)/3

Hence, verifying if int_a^b x^2 dx = (b^3 - a^3)/3 , yields that the given equality holds.

balajia | Student

int_a^b(x^2)dx = (x^3/3)_a^b = (b^3-a^3)/3