11-ImproperIntegrals11Aral\u0131k2015 - Atilim University OpenCourseWare Project Department of Mathematics Calculus I 1 Improper Integrals So far we

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Atilim University - OpenCourseWare Project - Department of Mathematics, Calculus I 1 Improper IntegralsSo far, we have integrated a continuous functionf(x)on a closed, bounded, °nite interval[a; b]. Wenote that such a function is bounded on the interval, and also, the integral is the area of a boundedregion provided thatf(x)is a positive function. We call it the proper integral.Now, we may ask to ourselves the following question:Question:Is it possible to °nd the area of the region under the curvesy=1x,y=1x2over theintervals(0;1]or[1;1)?To answer this question we want to discuss the following examples.Example 1Find the area region under the curvey=1x2, abovey= 0and to the right of the linex= 2.Z11 1
Atilim University - OpenCourseWare Project - Department of Mathematics, Calculus I