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Math Help - Antiderivative

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Konglomo View Post
    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 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 y= 5x^3- 23x^2- x+ 3 and y= 0, between x= 1/\sqrt{2} and 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 x^n is [tex]\frac{1}{n+1}x^{n+1}
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