The Relationship of the Tangent to a Curve and the Area under a CurveDate: 10/25/95 at 13:26:49 From: "betty.thompson" Subject: connection of tangent and finding area Lindsey Jahn is trying to find the answer to this problem. The problem of drawing a tangent to a given curve at a given point is closely connected with the problem of finding areas ("areas under a curve"). a. What is this connection? b. When was it discovered and by whom? Betty Thompson Date: 10/26/95 at 21:55:10 From: Doctor Jonathan Subject: Re: connection of tangent and finding area Lindsey: The tangent of a given curve at a point is the same thing as the slope of the curve at that point. The slope of a curve is also called the derivative of the curve (at any given point). On the other hand, the area under a curve is found via the operation of integration. The connection you may be looking for is the fact that the integral is exactly the opposite of the derivative. In fact, the integral is often referred to as the anti-derivative. So, the tangent is given by the derivative, and the area is given by the anti-derivative. All of this is basically just calculus, so the answer to your second question can probably best be answered as "When was calculus invented and by who?" Calculus was invented independently by Newton and Leibniz around 1666. -Doctor Jonathan, The Geometry Forum |
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