Transcription of Integral ch 7 - NCERT
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Integral ch 7 - NCERT
INTEGRALS 287vJust as a mountaineer climbs a mountain because it is there, soa good mathematics student studies new material becauseit is there. JAMES B. BRISTOL IntroductionDifferential Calculus is centred on the concept of thederivative. The original motivation for the derivative wasthe problem of defining tangent lines to the graphs offunctions and calculating the slope of such lines. IntegralCalculus is motivated by the problem of defining andcalculating the area of the region bounded by the graph ofthe a function f is differentiable in an interval I, , itsderivative f exists at each point of I, then a natural questionarises that given f at each point of I, can we determinethe function? The functions that could possibly have givenfunction as a derivative are called anti derivatives (orprimitive) of the function. Further, the formula that givesall these anti derivatives is called the indefinite Integral of the function and suchprocess of finding anti derivatives is called integration .
object at any instant, then there arises a natural question, i.e., can we determine the position of the object at any instant? There are several such practical and theoretical situations where the process of integration is involved. The development of integral calculus arises out of the efforts of solving the problems of the following types:
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