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<p>Find \(\displaystyle\int_{-4}^{2} \mathrm{f}(x) \, \mathrm{d}x - \displaystyle\int_{5}^{2} [\mathrm{f}(x) + 2x] \, \mathrm{d}x\), given that \(\displaystyle\int_{-4}^{5} \mathrm{f}(x) \, \mathrm{d}x = 4\).</p>

Find \(\displaystyle\displaystyle \displaystyle\int_{-4}^{2} \mathrm{f}(x) \, \mathrm{d}x - \displaystyle\displaystyle \displaystyle\int_{5}^{2} [\mathrm{f}(x) + 2x] \, \mathrm{d}x\), given that \(\displaystyle\displaystyle \displaystyle\int_{-4}^{5} \mathrm{f}(x) \, \mathrm{d}x = 4\).

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Integration

<p>Given that \(\displaystyle\int_{-6}^{3} \mathrm{f}(x) \, \mathrm{d}x = 6\), evaluate \(\displaystyle\int_{-6}^{-3} \mathrm{f}(x) - 1 \, \mathrm{d}x + \displaystyle\int_{-3}^{3} \mathrm{f}(x) \, \mathrm{d}x\).</p>

Given that \(\displaystyle\displaystyle \displaystyle\int_{-6}^{3} \mathrm{f}(x) \, \mathrm{d}x = 6\), evaluate \(\displaystyle\displaystyle \displaystyle\int_{-6}^{-3} \mathrm{f}(x) - 1 \, \mathrm{d}x + \displaystyle\displaystyle \displaystyle\int_{-3}^{3} \mathrm{f}(x) \, \mathrm{d}x\).

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

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

<p>Find \(\displaystyle\displaystyle \displaystyle\int_{-3}^{0} \mathrm{f}(x) \, \mathrm{d}x + \displaystyle\displaystyle \displaystyle\int_{0}^{2} \mathrm{f}(x) + 2 \, \mathrm{d}x\), given that&nbsp;\(\displaystyle\displaystyle \displaystyle\int_{-3}^{2} \mathrm{f}(x) \, \mathrm{d}x = 5\).</p>

Find \(\displaystyle\displaystyle \displaystyle\int_{-3}^{0} \mathrm{f}(x) \, \mathrm{d}x + \displaystyle\displaystyle \displaystyle\int_{0}^{2} \mathrm{f}(x) + 2 \, \mathrm{d}x\), given that \(\displaystyle\displaystyle \displaystyle\int_{-3}^{2} \mathrm{f}(x) \, \mathrm{d}x = 5\).

<p>Given that&nbsp;\(\displaystyle\displaystyle \displaystyle\int_{4}^{10} \mathrm{f}(x) \, \mathrm{d}x = 5\), find</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">\(\displaystyle\displaystyle \displaystyle\int_{4}^{10} 6\mathrm{f}(x) \, \mathrm{d}x\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list" start="2"><li><div class="list-item-paragraph">\(\displaystyle\displaystyle \displaystyle\int_{10}^{4}{\left[ \mathrm{f}\left( x \right)+\frac{1}{x} \right]\,\mathrm{d}x}\)  	</div></li></ol></div></div></div>

Given that \(\displaystyle\displaystyle \displaystyle\int_{4}^{10} \mathrm{f}(x) \, \mathrm{d}x = 5\), find

<p>Given that&nbsp;\(\displaystyle\displaystyle \displaystyle\int_{-2}^{5} \mathrm{f}(x) \, \mathrm{d}x = 14\), find</p>
<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list"><li><div class="list-item-paragraph">\(\displaystyle\displaystyle \displaystyle\int_{-2}^{5} 3\mathrm{f}(x) \, \mathrm{d}x\)</div></li></ol></div><div class="question-column" style="flex: 1; align-self: flex-start;"><ol class="abc-list" start="2"><li><div class="list-item-paragraph">\(\displaystyle\displaystyle \displaystyle\int_{5}^{-2} [\mathrm{f}(x) - 3x] \, \mathrm{d}x\)</div></li></ol></div></div></div>

Given that \(\displaystyle\displaystyle \displaystyle\int_{-2}^{5} \mathrm{f}(x) \, \mathrm{d}x = 14\), find

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