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In this paper you will learn the basic integration rule from the basic differentiation rule.Last time we have learned anti-derivative,indefinite integral,and the power rule in integration.Let us recall what the power rule in differentiation is.If n is a real number,and y=xn,then y’=nxn-1.Proof:Let y=xn,we get ln|y|=ln|xn|,Since ln|xn|=n ln|x|,so we get ln|y|=n ln|x|.Take differentiation for both side above:y’y=n x.
In this paper you will learn the basic integration rule from the basic differentiation rule. Last time we have learned anti-derivative, indefinite integral, and the power rule in integration. Let us recall what the power rule in differentiation is. If n is a real number, and y = xn, then y ’= nxn-1.Proof: Let y = xn, we get ln | y | = ln | xn |, Since ln | xn | = n ln | x |, so we get ln | y | = n ln | x |. Take differentiation for both side above: y’y = n x.