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February 22nd, 2017, 09:02 AM   #1
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Question Calculate area of grade two function using integral?

My mathematics book gave me an assignment to calculate the area using an integral there a = 0, b = 2. I succeeded to calculate the area and get to the correct answer. But when I checked which area I was calculating it wasn't inside the function. So now I wonder how to calculate the area inside the x^2 function.

But the value of a and b have to change to do that I guess. But I have no idea of how to start calculating the inside area if it is possible.

$\displaystyle
\int_{a}^{b} x^2 dx
$
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Last edited by DecoratorFawn82; February 22nd, 2017 at 09:04 AM.
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February 22nd, 2017, 09:09 AM   #2
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There is no "area inside the graph of $\displaystyle y= x^2$" unless you have an upper boundary! If you were asked to find the area above the graph $\displaystyle y= x^2$ and below the line y = 4, from x = -1 to 1, then each vertical line, at given x, will have length $\displaystyle 4- x^2$. We can think of that as an "infinitesimally thin" rectangle with height $\displaystyle 4- x^2$ and with "dx". The area of that rectangle is $\displaystyle (4- x^2) dx$ and the entire area will be the "sum" (integral) of all those, $\displaystyle \int_{-1}^1 (4- x^2) dx$.
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Last edited by skipjack; February 22nd, 2017 at 11:21 AM.
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