Integration and Antidifferentiation, Exercises of Elementary Mathematics

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MGT

LECTURE – 25

Here the dark region is area under the curve y=f(x) in the interval [a,b].

Here to find the area under the curve, we have to find a function A(x) whose derivative is f(x). i.e. This process of finding A(x) is called antidifferentiation problem. By simple guessing we see that If we agree that the area above a singe point Should be taken as zero, then on putting A(0) = 0 , And x=0, we get C=0. So we can write

If we differentiate an antiderivative of f(x) , we obtain f(x) back again. Thus Part (b) and (c) of theorem 5.2.3 can be extend to more than two Functions, which in combination with part (a) results in the following General formula: