Question

integrala de la a la 0 din x+2= integrala de la 6-a si 0 din x+2 - 4

Answer 1

[tex]\\ x+2-4 = \boxed{x-2} =\ \textgreater \ \int^a_0(x+2)dx = \int^{6-a}_0 (x-2) dx \\ \\ \\ \int^a_0(x+2)dx = \frac{x^2}{2} - 2x|^a_0 = \boxed{\frac{a^2}{2} -2a} \\ \\ \\\int^{6-a}_0 (x-2) dx = \boxed{\frac{(6-a)^2}{2}-2(6-a)} \\ \\ \\\frac{a^2}{2} -2a = \frac{(6-a)^2}{2}-2(6-a) =\ \textgreater \ \\ \\ =\ \textgreater \ \frac{a^2-4a}{2} = \frac{36 - 24 + a^2 + 4a - 12a }{2} \\ =\ \textgreater \ \frac{a^2-4a}{2} = \frac{12-8a+a^2}{2} = 6 -4a + \frac{a^2}{2} \\ =\ \textgreater \ \frac{a^2}{2} - 4a + 6 = \frac{a^2}{2} +2a \\ =\ \textgreater \ 6a = 6 \\ =\ \textgreater \ \boxed{a=1}[/tex]