Question

Calcule a área abaixo de f(x)=x²+10x entre x=0 e x= 10

Answer 1

$\displaystyle \sf f(x)=x^2+10x$

área do gráfico entre 0x = 0 e x = 10, então vamos integrar de 0 a 10

$\displaystyle \sf \int\limits^{10}_{0}( x^2+10x)dx \\\\\\ \int\limits^{10}_0x^2dx +\int\limits^{10}_010xdx \\\\\\ \left\frac{x^3}{3}\right|^{10}_0+\left \frac{10x^2}{2}\right|^{10}_0 \to\left\frac{x^3}{3}\right|^{10}_0+\left \frac{5x^2}{1}\right|^{10}_0 \\\\\\ \frac{10^3}{3}-\frac{0^3}{3}+\frac{5\cdot 10^2}{1}-\frac{5.0^2}{1} \\\\\\ \frac{1000}{3} +5\cdot 100 \\\\\\ \frac{1000+1500}{3} = \frac{2500}{3} \approx 83,33$

$\displaystyle \sf Portanto :\\\\ \boxed{\sf \displaystyle \sf \int\limits^{10}_{0}( x^2+10x)dx \approx 83,33\ }$