[tex]f(x)=x^{2}-4[/tex]
a)
Vezi tabelul de integrale din atasament
[tex]\int\limits^3_0 {x^2} \, dx =\frac{x^3}{3} |_0^3=\frac{27}{3} -0=9[/tex]
b)
[tex]\int\limits^1_0 {\frac{1}{x^2+1} } \, dx =arctgx|_0^1=arctg1-arctg0=\frac{\pi}{4}[/tex]
c)
a>0
[tex]\int\limits^a_{\frac{1}{a}} \frac{1}{x^2} -4\ dx=\int\limits^a_{\frac{1}{a}} x^{-2}\ dx-\int\limits^a_{\frac{1}{a}} 4\ dx=-x^{-1}|^a_{\frac{1}{a}}-4x|^a_{\frac{1}{a}}=-\frac{1}{a}+a-4a+\frac{4}{a}=\frac{3}{a} -3a[/tex]
[tex]\frac{3}{a} -3a=-8[/tex]
Aducem la acelasi numitor comun a
3-3a²=-8a
3a²-8a-3=0
Δ=64+36=100
[tex]a_1=\frac{8+10}{6} =3\\\\ a_2=\frac{8-10}{6} =\frac{-1}{3} < 0\ NU[/tex]
a=3
Un alt exercitiu cu integrale gasesti aici: https://brainly.ro/tema/9918989
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