Bonjour Design971
[tex]\int\limits^4_0 {(5x^{2}-8x+4)} \, dx=...[/tex]
Nous savons que
[tex]\int5x^2\,dx=5\int x^2\,dx=5\times\dfrac{x^3}{3}+C=\dfrac{5x^3}{3}+C\\\\\int(-8x)\,dx=-8\int x^1\,dx=-8\times\dfrac{x^2}{2}+C=-4x^2+C\\\\\int 4\,dx=4x+C[/tex]
Donc
[tex]\int\limits^4_0 {(5x^{2}-8x+4)} \, dx\\\\=[\dfrac{5x^3}{3}-4x^2+4x]\limits^4_0\\\\=(\dfrac{5\times4^3}{3}-4\times4^2+4\times4)-(\dfrac{5\times0^3}{3}-4\times0^2+4\times0)\\\\=(\dfrac{320}{3}-64+16)-(0)\\\\=\dfrac{176}{3}[/tex]
Par conséquent,
[tex]\boxed{\int\limits^4_0 {(5x^{2}-8x+4)} \, dx=\dfrac{176}{3}}[/tex]
