`int_a^bxdx = (b^2 - a^2)/2` Prove that

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to use the fundamental theorem of calculus, to prove the equality, such that:

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

You need to replace x for f(x), such that:

`int_a^b xdx = x^2/2|_a^b`

`int_a^b xdx = b^2/2 - a^2/2`

`int_a^b xdx = (b^2-a^2)/2`


Hence, checking the given equality yields that `int_a^b xdx = (b^2-a^2)/2` holds.

balajia | Student

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