Question

Encontre a área da região assombreada.

Answer 1

Teorema Fundamental  do Cálculo  parte 1

$\Large\boxed{\boxed{\displaystyle\mathsf{\int\limits_{a}^{b} f(x)dx=g(x)\Bigg|_a^b}}}$

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$\displaystyle\mathsf{A=\int\limits_{0}^{4}(5x-x^2-x)~dx=\int\limits_{0}^{4}(4x-x^2)~dx}$

$\mathsf{A=2x^2-\dfrac{1}{3}x^3\Bigg|_{0}^4}\\\mathsf{A=2\cdot4^2-\dfrac{1}{3}\cdot4^3}\\\mathsf{A=32-\dfrac{64}{3}=\dfrac{96-64}{3}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{A=\dfrac{32}{3}~u\cdot a}}}}}$      

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