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Using calculus, find the formula for the area of a rectangle.

Say we have a rectangle of length a and height b. We know that the area is given by the simple formula A=ab but now that we know calculus we can derive this formula and many others. Set up the rectangle so that it is completely in the first quadrant but has one edge against the x-axis and another up against the y-axis. Then the area can be found by an integral

A=\int _{{0}}^{{a}}b\,dx=bx{\bigg |}_{{0}}^{{a}}=b(a)-b(0)=ab\,

Thus, by calculus we can find the equation which gives the area of a rectangle.

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