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Why is integration the area under a curve (graphically)? Derivative gives the slope which makes perfect sense as it shows the change at a point. But how is, its opposite, the integral represented by the area under the curve.

Asutosh Swain
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    What definition of integration are you using? It's quite clear from the Riemann sums definition. – Cameron L. Williams Mar 24 '15 at 04:47
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    If you're looking for reasoning that the Anti-Derivative finds the area under a curve, there is some good discussion and graphics on this question http://math.stackexchange.com/questions/15294/why-is-the-area-under-a-curve-the-integral – turkeyhundt Mar 24 '15 at 04:48

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The integral as a limit of Riemann sums DEFINES the area under a curve. You can COMPUTE the integral by computing the anti derivative and applying the fundamental theorem of calculus. But the integral is the definition of area.