Jika [tex] \int\limits^4_1 {f(x)} \, dx =6[/tex] maka [tex] \int\limits^4_1 {f(5-x)} \, dx =...[/tex]

Bab Integral
Matematika SMA Kelas XII

f(x) = ax + b

 ₄
∫  (ax + b) dx = 6
¹
                     ₄
(a/2) x² + bx |    = 6
                     ¹
(a/2) 4² + 4b - (a/2) 1² - b . 1 = 6
8a + 4b - (a/2) - b = 6
(15/2) a + 3b = 6
***dikalikan 2***
15a + 6b = 12
5a + 2b = 4
 
f(5 - x) = a (5 - x) + b
f(5 - x) = 5a - ax + b

₄
∫ f(5 - x) dx
¹                                    ₄
= ((-a/2) x² + 5ax + bx) |
                                      ¹
= (-a/2) . 4² + 5 . a . 4 + b . 4 + (a/2) 1² - 5a . 1 + b .1
= -8a + 20a + 4b + (a/2) - 5a - b
= (15/2) a + 3b
= (3/2) (5a + 2b)
= (3/2) . 4
= 6