Question

Determine la integral definida:

∫_(-3)^5 |x| dx

Answer 1

$\displaystyle \int_{ - 3}^{5} |x| dx = \displaystyle \int_{ - 3}^{0} - xdx + \int_{0}^{5}xdx \\ = - \dfrac{ {x}^{2} }{2} \big|_{ - 3}^{0} + \frac{ {x}^{2} }{2} \big|_{0}^{5} = - \frac{9}{2} + \frac{25}{2} = \frac{16}{2} = 8$

Cuando veas valor absoluto siempre separa en dos integrales, eso.

Espero te sirva, saludos!