Question

Determinati primitiva F a functiei f pentru ca F(1)=2015

Answer 1

F(x)=∫(4x³+3x²)dx=4∫x³dx+3∫x²dx.
se  aplica  formula
∫x^ndx=x^(n+1)/(n+1)
F(x)=4·x^4/4+3x³/3+c=x^4+x^3+C
F(1)=1^4+1^3+C=2015=>1+1+C=2015
2+C=2015
C=2015-2=2013
F(x)=x^4+x^3+2013

Answer 2

$F(x) = \int\limits {f(x)} \, dx \\ F(x) = \int\limits {(4 x^{3} + 3x^{2}) } \,dx \\ F(x) = 4* \frac{ x^{4} }{4} + 3 *\frac{ x^{3} }{3} + C\\ F(x) = x^{4} + x^{3} + C\\ F(1) = 1 + 1 + C\\ F(1) = 2 + C$

F(1) = 2 + C => 2015 = 2 + C =>C = 2013

=> $F(x) = x^{4} + x^{3} + 2013$    (solutia problemei)