Integrais Definidas - Exercício

Prévia do material em texto

Exercícios 
 
Integrais Definidas 
 
 10 
a) ∫1 4dx 
 10 10 
∫1 4dx = 4x = 4.10 – 4.1 = 40 – 4 = 36 
 1 
 
 1 
b) ∫0 1xdx 
 2 
 
 1 1 
∫0 1xdx = 1 . x2 = x2 = 12 - 02 = 1 
 2 2 2 4 0 4 4 4 
 
 
 1 
c) ∫-1 x2dx 
 
 1 1 
∫-1 x2dx = x3 = 13 – (-13) = 2 
 3 -1 3 3 3 
 
 
 
 0 
d) ∫-1 x3dx 
 
 0 0 
∫-1 x3dx = x4 = 04 - (-14) = 1 
 4 -1 4 4 4 
 
 
 
 
 
 
 2 
e) ∫0 (x2 + 3)dx 
 
 2 2 
∫0 (x2 + 3)dx = x3 + 3x = ( 23 + 3.2 ) – (03 + 3.0) = 14 
 3 0 3 3 3 
 
 
 1 
f) ∫0 (1 x2 + 5x + 1)dx 
 4 
 
 1 1 
∫0 (1 x2 + 5x + 1)dx = x3 + 5x2 + x = (13 + 5.12 + 1) – (03 + 5.03 + 0) = 
 4 12 2 0 12 2 12 3 
 
 
= 1 + 5 + 1 = 1 + 30 +12 = 43 
 12 2 12 12 
 
 
 9 
g) ∫0 √x dx 
 
 9 9 
∫0 √x dx = x3/2 = 2x3/2 = 2.93/2 – 2.03/2 = 2.√93 = 2 . 27 = 18 
 3 3 0 3 3 3 3 
 2 
 
 
 
 
 
 
 93/2 = √93