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  4. underset h arrow 0 textLim (∫ limits a x + h ln 2 tdt -∫ limits a x ln 2 tdt / h )=

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Q. $\underset { h \rightarrow 0}{\text{Lim}} \frac{\int\limits_{ a }^{ x + h } \ln ^2 tdt -\int\limits_{ a }^{ x } \ln ^2 tdt }{ h }=$

Integrals

Solution:

Differentiating w.r.t. h
$\underset {h \rightarrow 0}{\text{Lim}} \frac{\ln ^2(x+h)-\ln ^2(a) \cdot 0-0}{1}=\ln ^2 x$