Bagaimana untuk menyelesaikannya? Int_2 ^ 85-xdx =?

Jawapan:

#= 9#

Penjelasan:

# int_2 ^ 8 | 5-x | dx = int_2 ^ 5 (5-x) dx + int_5 ^ 8 (x-5) dx #

# = 5x - x ^ 2/2 + C1 _2 ^ 5 + x ^ 2/2 - 5x + C2 _5 ^ 8 #

# = 12.5 + C1 - 8 - C1 - 8 + C2 + 12.5 - C2 #

#= 9#

# "Pada langkah pertama kami hanya menerapkan takrif | … |:" #

# | x | = {(-x, "," x <= 0), (x, "," x> = 0):} #

# "Jadi" #

# | 5 - x | = {(x - 5, "," 5-x <= 0), (5 - x, "," 5-x> = 0):} #

# = {(x - 5, "," x> = 5), (5 - x, "," x <= 5):} #

# "Jadi kes had x = 5 membelah selang integrasi dalam dua" #

# "bahagian: 2, 5 dan 5, 8." #