Question

$\int\limits^8_6(x^2-6x) \, dx$

Answer 1

Temos uma integral definida 

Primeiro calculamos a integral e em seguida limitamos ... 

Limite superior menos limite inferior 

Resolvendo ... 

$\int\limits^8_6 {(x^{2}-6x)} \, dx \\\\\\ \frac{x^{2+1}}{2+1}- \frac{6x^{1+1}}{1+1} \\\\\\\frac{x^{3}}{3} - \frac{6x^{2}}{2} \\\\\\ \boxed{ \frac{x^{3}}{3} -3x^{2}}\\\\\\Agora\ aplico\ os\ limities\ :$

$| \frac{8^{3}}{3} -3.8^{2}|\ -\ | \frac{6^{3}}{3} -3.6^{2}|\\\\\\| \frac{512}{3} -3.64|\ -\ | \frac{216}{3} -3.36|\\\\\\| \frac{512}{3}- \frac{216}{3} -192+108|\\\\\\ \frac{296}{3} -84\\\\\\ \frac{296}{3} - \frac{252}{3} =\boxed{\boxed{ \ \frac{44}{3}\ }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$