Question

Determine a área da região entre a curva dada e o eixo x, nos intervalos dados:


y = √x, [2, 5]

Answer 1

Basta calcular a integral definida neste intervalo:

$A=\int_2^5\sqrt{x}\;dx$

$A=\int_2^5x^{1/2}\;dx$

$A=\left[\frac{x^{1/2+1}}{1/2+1}\right]_2^5$

$A=\left[\frac{x^{3/2}}{3/2}\right]_2^5$

$A=\left[\frac{2x^{3/2}}{3}\right]_2^5$

$A=\frac{2\cdot5^{3/2}}{3}-\frac{2\cdot2^{3/2}}{3}$

$A=\frac{10\sqrt{5}-4\sqrt{2}}{3}\text{ u.a}$