1)\( \int_{2}^5 2\, dx \)
\( 10-4=6\)
2)\( \int_{1}^{3} x^3\, dx\)
\( \frac{81}{4}- \frac{1}{4}=20\)
3)\( \int_{2}^{3} -4x^3\, dx\)
\(-81-{-16}=-65 \)
4)\( \int_{3}^{5} (3x+6)\, dx\)
\(( \frac{75}{2}+30)-(\frac{27}{2}+18)=36\)
5)\( \int_{1}^{3} \frac{2}{x^6} \, dx\)
\( -\frac{2}{1215}--\frac{2}{5}=\frac{484}{1215}\)
6)\( \int_{4}^{9} (1+ \sqrt{x}) \, dx\)
\( \left(9+ \frac{2}{3}(27) \right)- \left(4+ \frac{2}{3}(8) \right)= \frac{53}{3}\)
7)\( \int_{1}^{2} \left(\frac{2}{x^2}-\frac{3}{\sqrt{x}} \right) dx\)
\( \left(-\frac{2}{2}-\sqrt{2}\right)- \left(-\frac{2}{1}-6 \right)=7-6\sqrt{2}\)
8)\(\int_{0}^{1} \frac{\sqrt{x}(x^2+3)}{\sqrt[3]x} \, dx\)
\( \left(\frac{6}{19}+\frac{18}{7} \right)- \left(0-0 \right)= \frac{384}{133}\)