1. ## Antiderivative

I'm trying to find the area between the antiderivative of the curve y = 5x3 - 23x2 - x + 3 passing through the point (1, e) and the x-axis from x = 1/√2 to x = 17π/11, to 3 significant figures. I'm fairly new to this, so any explanations would also be greatly appreciated.

2. Originally Posted by Konglomo
I'm trying to find the area between the antiderivative of the curve y = 5x3 - 23x2 - x + 3 passing through the point (1, e) and the x-axis from x = 1/√2 to x = 17π/11, to 3 significant figures. I'm fairly new to this, so any explanations would also be greatly appreciated.
Do you mean $\displaystyle y= 5x^3- 23x^2- x+ 3$. If you don't want to use LaTex, it is standard to use "^" to indicate powers.

Are you sure you have copied the problem correctly? Strictly speaking a curve does not have an anti-derivative nor is there an "area" assigned to an anti-derivative.

My first thought was that you were asked to find the area between the curve corresponding $\displaystyle y= 5x^3- 23x^2- x+ 3$ and y= 0, between $\displaystyle x= 1/\sqrt{2}$ and $\displaystyle x= 17\pi/11$, by finding the anti-derivative of that function.

However, the "passing through the point (1, e)" makes me think you are first to find the anti-derivative of that function, using the condition that y(1)= e to determine the constant of integration, then integrating again to find the area.

You should be able to do that using the fact that the anti-derivative of $\displaystyle x^n$ is [tex]\frac{1}{n+1}x^{n+1}