Răspuns:
a) [tex]\displaystyle\int_0^3(f(x)+4)dx=\int_0^3x^2dx=\left.\frac{x^3}{3}\right|_0^3=9[/tex]
b) [tex]\displaystyle\int_0^1\frac{1}{f(x)+5}dx=\int_0^1\frac{1}{x^2+1}dx=\left. \arctan x\right|_0^1=\displaystyle\frac{\pi}{4}[/tex]
c) [tex]\displaystyle\int_{\frac{1}{a}}^af\left(\frac{1}{x}\right)dx=\int_{\frac{1}{a}}^a\left(\frac{1}{x^2}-4\right)dx=\left. -\frac{1}{x}\right|_{\frac{1}{a}}^a-\left. 4x\right|_{\frac{1}{a}}^a=\frac{-3a^2+3}{a}=-8[/tex]
Rezultă [tex]a=3[/tex].
Explicație pas cu pas:
