Question

A integral definida da função vetorial r(t) = (t² - 1)i + (2t +1)j + (t³)k para t pertencente ao intervalo [0,2] é:
a) 〈6, 4/3, 4 〉
b) 〈 2/3, 6, 4 〉
c) 〈4, 5, 2/3 〉
d) 〈2, 2/3 ,6 〉
e) 〈 4/3, 4, 5 〉

Answer 1

Bom dia 

r(t) = (t² - 1)i + (2t +1)j + (t³)k 

integral

R(t) = (t³/3 - t)i + (t² + t)j + (t⁴/4)k 

R(0) = 0i + 0j + 0k 
R(2) = (8/3 - 2)i + (4 + 2)j + (4)k 
R(2) = (2/3)i + (6)j + (4)k 

b) 〈 2/3, 6, 4 〉