<p>Given that \(\displaystyle\int\nolimits_{0}^{\ln 2} \mathrm{f}(x) \, \mathrm{d}x = 8\), evaluate \(\displaystyle\int\nolimits_{0}^{\frac{1}{2}} \mathrm{f}(x) + e^{2x} \, \mathrm{d}x + \displaystyle\int\nolimits_{\frac{1}{2}}^{\ln 2} \mathrm{f}(x) + e^{x} \, \mathrm{d}x\) exactly.</p>

Given that \(\displaystyle\displaystyle \displaystyle\int\nolimits_{0}^{\ln 2} \mathrm{f}(x) \, \mathrm{d}x = 8\), evaluate \(\displaystyle\displaystyle \displaystyle\int\nolimits_{0}^{\frac{1}{2}} \mathrm{f}(x) + e^{2x} \, \mathrm{d}x + \displaystyle\displaystyle \displaystyle\int\nolimits_{\frac{1}{2}}^{\ln 2} \mathrm{f}(x) + e^{x} \, \mathrm{d}x\) exactly.

Definite Integrals and Area under graph - Understanding Results of Definite Integrals

Question 0a1a7d39

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