Integrate x + pi dx between pi and -pi
thanks
If you want help with a calculus problem, don't put it in the pre-calculus section!
So, what's the difficulty? The integral of x is $\displaystyle \tfrac12x^2$, the integral of $\displaystyle \pi$ (being a constant) is $\displaystyle \pi x$. Add them together, evaluate the result at $\displaystyle \pi$ and $\displaystyle -\pi$, and take the difference.
To solve the integral, raise x to the second power and divide it by 2, and add an x to pi to get:
(2x)/2 + pi(x) + C
Now just solve the integral for pi to -pi, so you would just sub in and solve by subtracting the second number solved in the indefinite integral, minus the first.
((2pi)/2 + pi(pi)) - ((2(-pi)/2 + pi(-pi))
(4pi)/2 + 2(pi)^2
You just said "raise x to the second power" but now you write "2x"!
That should be $\displaystyle x^2/2+ pi x+ C$
And apparently that was not just a typo since you now calculate 2 times pi rather than squareing. You should haveNow just solve the integral for pi to -pi, so you would just sub in and solve by subtracting the second number solved in the indefinite integral, minus the first.
((2pi)/2 + pi(pi)) - ((2(-pi)/2 + pi(-pi))
(4pi)/2 + 2(pi)^2
$\displaystyle (pi)^2/2+ pi(pi)- ((-\pi)^2/2- pi(-pi))= 2pi^2$