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**Week 10: Using integral in finding Areas**

The **area** under a curve between two points can be found by doing a definite **integral** between the two points. To **find** the **area** under the curve y = f(x) between x = a and x = b, **integrate** y = f(x) between the limits of a and b. **Areas** under the x-axis will come out negative and **areas** above the x-axis will be positive.Since we are assuming that f is continuous on [0,a], it is continuous on the interval with endpoints b and b+h (I say it this way because h could be negative). ... Then m(h)≤f(x)≤M(h) for all x in the interval, so we know, since the integral is the **area. **A double **integral** over three coordinates giving the **area** within some region , If a plane curve is given by , then the **area** between the curve and the x-axis from to is given by. SEE ALSO: **Integral**, Line **Integral**, Lusin **Area Integral**, Multiple **Integral**, **Surface Integral**, Volume **Integral**.If a function is strictly positive, the **area between** it and the x axis is simply the **definite integral**. If it is simply negative, the **area** is -1 times the **definite integral**. ... First the **area between** y=f of x some curve and the x axis from x=a to x=b.