Question

Analiza matematica clasa a XII-A M2​

Answer 1

Acesta este răspunsul meu.

Answer 2

a) $f(x)-x-1=x^4+x+1-x-1=x^4\\\int\limits^1_0 {x^4} \, dx =\frac{x^5}{5}|_0^1=\frac{1}{5}-0=\frac{1}{5}$

b)$\int\limits^e_1 ({f(x)-x^4-1})lnx\, dx=\int\limits^e_1( {x^4+x+1-x^4-1})lnx \, dx =\int\limits^e_1 {x} lnx\, dx=\int\limits^e_1 {(\frac{x^2}{2} })'lnx \, dx =\frac{x^2}{2}lnx|_1^e-\frac{1}{2}\int\limits^e_1 {x^2*(lnx)'} \, dx=\frac{e^2}{2} -\frac{1}{2} \int\limits^e_1 {x^2*\frac{1}{x} } \, dx } =\frac{e^2}{2} -\frac{1}{2}*\frac{x^2}{2}|_1^e=\frac{e^2}{2} -\frac{e^2}{4} +\frac{1}{4} =\frac{e^2+1}{4}$

c)$\int\limits^1_0 {x^4+x+1} \, dx =\frac{x^5}{5}|_0 ^1 +\frac{x^2}{2}|_0^1 +x|_0^1=\frac{1}{5}-0+\frac{1}{2}-0+1-0=\frac{17}{10}$