Question

Find the integral.

Answer 1

\[\large \int\limits_{-1}^1 x^3-2x+3 \; dx\]
We'll want to apply the `Power Rule for Integration` to each term.
\[\large \int\limits x^n\;dx \qquad = \qquad \dfrac{x^{n+1}}{n+1}\]We increase the power by 1, and then divide by the new power.
I prefer to write it this way, with the coefficient as a fraction in front.\[\large = \frac{1}{n+1}x^{n+1}\]

Answer 2

Applying this rule to the first term will give us,\[\large x^3 \qquad \rightarrow \qquad \frac{1}{3+1}x^{3+1} \qquad \rightarrow \qquad \frac{1}{4}x^4\]

Answer 3

Understand the process? Think you can do the others? :)

Answer 4

I got \[(1/4)x^4-x^2 +3x \] as the antiderivative.

Answer 5

I plug in the 1 and -1. I get 8 but wolfram is telling me it's 6. I wanted to check with someone else.

Answer 6

Yah I'm coming up with 6 also.

My guess is that you forgot that \((-1)^4\) and \((-1)^2\) give you a \(+1\).
Is there where the mistake was maybe? :o