[tex]f(x)=x^{2}+\frac{x}{\sqrt{x^{2}+9}}[/tex]
a)
Vezi tabel de integrale in atasament
[tex]\int\limits^1_0 {x^2} \, dx =\frac{x^3}{3}|_0^1=\frac{1}{3}[/tex]
b)
[tex]\int\limits^4_0 { x^2+\frac{x}{\sqrt{x^2+9} } -x^2+\frac{x}{\sqrt{x^2+9} } } \, dx =\int\limits^4_0 {\frac{2x}{\sqrt{x^2+9} } } \, dx =2\sqrt{x^2+9} |_0^4=10-6=4[/tex]
c)
[tex]\int\limits^a_4 {x+\frac{1}{\sqrt{x^2+9} } } \, dx =\frac{x^2}{2}|_4^a+ln(x+\sqrt{x^2+9} )|_4^a=\frac{a^2}{2} -8+ln(a+\sqrt{a^2+9})-ln9 \\\\\frac{a^2}{2} -8+ln(a+\sqrt{a^2+9})-ln9 =10+ln\frac{a+\sqrt{a^2+9} }{9} \\\\\frac{a^2}{2}-8=10\\\\ \frac{a^2}{2}=18\\\\ a=6\\\\sau\\\\a=-6[/tex]
Un alt exercitiu cu integrale gasesti aici: https://brainly.ro/tema/9918948
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