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

Expert Answers
sciencesolve eNotes educator| 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`


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