Question

O valor da Integral Definida $\int\limits^1_-1 (x^7+x^3+x)dx$ é:

a) 1/4

b) 1/2

c) 0

d) 1/8

e) 9/2

Answer 1

$\int\limits^1_{-1} ({x^{7}+x^{3}+x)} \, dx \\\\\\integrando...\\\\\\ \frac{x^{7+1}}{7+1} + \frac{x^{3+1}}{3+1} + \frac{x^{1+1}}{1+1} \\\\\\ \boxed{\boxed{\frac{x^{8}}{8} + \frac{x^{4}}{4} + \frac{x^{2}}{2} \ +\ c}}$


Agora fazemos índice superior menos inferior ... 


$|( \frac{x^{8}}{8}+ \frac{x^{4}}{4} + \frac{x^{2}}{2} ) |-|( \frac{x^{8}}{8} + \frac{x^{4}}{4} + \frac{x^{2}}{2} )|\\\\\\|( \frac{1^{8}}{8} + \frac{1^{4}}{4} + \frac{1^{2}}{2} )|-|( \frac{(-1)^{8}}{8} + \frac{(-1)^{4}}{4} + \frac{(-1)^{2}}{2} )|\\\\\\|( \frac{1}{8} + \frac{1}{4} + \frac{1}{2} )|-|( \frac{1}{8} + \frac{1}{4} + \frac{1}{2} )|\\\\\\| \frac{7}{8} |- |\frac{7}{8}| \ =\boxed{\boxed{\ \ \ 0\ \ \ }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ Letra\ \ c)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$