Question

A área limitada pela curva f(x)= x^2-4 e as retas x=0 e x=4 é dada por?

Answer 1

A área será dada pela soma de A₁ com A₂, que é a mesma área calculada pela integral abaixo:

$\boxed{\boxed{S=\int\limits_{0}^{4}x^{2}-4dx}}$
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$S=\int\limits_{0}^{4}x^{2}-4dx\\\\\\S=\left\dfrac{x^{2+1}}{2+1}-\dfrac{4x^{0+1}}{0+1}\right]\limits_{0}^{4}\\\\\\S=\left\dfrac{x^{3}}{3}-4x\right]\limits_{0}^{4}\\\\\\S=\dfrac{4^{3}}{3}-4\cdot4-\left(\dfrac{0^{3}}{3}-4\cdot0\right)\\\\\\S=\dfrac{64}{3}-16\\\\\\S=\dfrac{64-48}{3}\\\\\\\boxed{\boxed{S=\dfrac{16}{3}}}$