Question

O valor da integral 2016.2-U1S2-AAP-CDI3-Q6.jpg é:

Escolha uma:
a. 1/7
b. 1/8
c. 1/6
d. 1/5
e. 1/4

Answer 1

$\displaystyle \sf \int\limits^1_0\left[\int\limits^{x}_{x^{2}} dy \right]dx \\\\\\ \int\limits^1_0\left(\left\frac{y}{} \right|\limits^{x}_{x^{2}}\right)dx \\\\\\ \int\limits^1_0(x-x^2 )dx \\\\\\ \int\limits^1_0 xdx -\int\limits^1_0 x^2dx \\\\\\ \left \frac{x^2}{2}\right|\limits^1_0-\left \frac{x^3}{3}\right|\limits^1_0 \\\\\\ \frac{1^2}{2}-\frac{0^2}{2}-\left(\frac{1^3}{3}-\frac{0^3}{3}\right) \\\\\\ \frac{1}{2}-\frac{1}{3} \\\\\\\\ \huge\boxed{\ \sf \frac{1}{6}\ }\checkmark$

letra c