Antiderivative/Intergral of x^2 on interval [1, 2]

[needurhelp]

I need help on finding the antiderivative of x^2 on the interval [1, 2]

Here is what I have so far:

. . .integral x^2 dx
. . .=
. . .(x^3)/3
. . .=
. . .1/3

I'm not sure if what I'm doing is right. If it is, I don't know what to do with the interval [1, 2].

 

[stapel]

How did you get that x³/3 equalled 1/3? (This would require that x always be equal to 1, which is not specified in the exercise.)

When antidifferentiation was covered in class, the instructor (and the text) should have mentioned what to do with the limits. (It's one of the "Fundamental Theorems", after all!)

. . . . .For F(x) such that F'(x) = f(x) for all x in [a, b], we have

. . . . . . . .int[a, b] [f(x)] dx = F(b) - F(a)

In other words, integrate; then evaluate the integral at either endpoint, and subtract the lower-end value from the upper-end value.

Eliz.

 

[needurhelp]

ok thanks i got it.