**Integration the Area Problem Calculus Socratic**

areas under curves & the definite integral Suppose you were asked to estimate the shaded area under the curve shown below. A simple and effective way to estimate the shaded area is to add the areas of narrow rectangles of equal widths, that span the interval: [ a, b ] and with heights that match the values of " " at appropriate values of " x " on the interval.... We have seen that the definite integral, the limit of a Riemann sum, can be interpreted as the area under a curve (i.e., between the curve and the horizontal axis). This applet explores some properties of definite integrals which can be useful in computing the value of an integral.

**The Definite Integral Worcester Polytechnic Institute**

The definite integral of a function f(x) from a to b is the signed area under the curve between a and b. If the function is positive, the signed area is positive, as before (and we can call it area.) If the function dips below the x-axis, the areas of the regions below the x-axis come in with a negative sign.... Finally, whether we think of the area between two curves as the difference between the area bounded by the individual curves (as in ) or as the limit of a Riemann sum that adds the areas of thin rectangles between the curves (as in ), these two results are the same, since the difference of two integrals is the integral of the difference:

**Definite integrals are used to find the area between a**

Section 6.1: Definite Integral Suppose we want to find the area of a region that is not so nicely shaped. For example, consider the function shown below. The area below the curve and above the x axis cannot be determined by a known formula, so we’ll need a method for approximating the area. Suppose we want to find the area under the parabola and above the x axis, between the lines x = 2 and how to make yourself look younger with makeup The area under a curve is the area between the curve and the x-axis. The curve may lie completely above or below the x-axis or on both sides. In calculus, you measure the area under the curve using definite integrals.

**Definite Integral UH**

Section 6.1: Definite Integral Suppose we want to find the area of a region that is not so nicely shaped. For example, consider the function shown below. The area below the curve and above the x axis cannot be determined by a known formula, so we’ll need a method for approximating the area. Suppose we want to find the area under the parabola and above the x axis, between the lines x = 2 and how to get your braces off faster with rubber bands Brightstorm explains how to use definite integrals to find area. There are two basic area problems: one in which the area lies between the function and the x-axis, and one where the area lies between …

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### 5.3 The De nite Integral as Area Arkansas Tech University

- The definite integral- area under a curve Mathematics
- The Definite Integral Worcester Polytechnic Institute
- The Definite Integral Worcester Polytechnic Institute
- Use a definite integral to find the area of the region

## How To Find Area Between The Curve With Definite Integral

18/08/2008 · Best Answer: Assuming that you want to find the area above the x-axis, the idea is that you want to integrate under the curve along the domain that is in positive y. The integral is like summing up the bits of area under the curve so you just need to define the limits properly.

- 18/08/2008 · Best Answer: Assuming that you want to find the area above the x-axis, the idea is that you want to integrate under the curve along the domain that is in positive y. The integral is like summing up the bits of area under the curve so you just need to define the limits properly.
- 5.3 THE DEFINITE INTEGRAL AS AREA 1 5.3 The De nite Integral as Area In this section, we will see how de nite integrals are used to nd areas. Case 1:f(x) 0
- Since we know how to get the area under a curve here in the Definite Integrals section, we can also get the area between two curves by subtracting the bottom curve from the top curve everywhere where the top curve is higher than the bottom curve.
- A definite integral as the area under the function $ f(x) $ between $ a $ and $ b $ The definite integral, when $ \int\limits_a^b f(x)dx $ is the area between the function $ f(x) $ and the x-axis where $ x $ ranges from $ a $ to $ b $.