beserta caranya kalau bisa
Matematika
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Pertanyaan
beserta caranya kalau bisa
1 Jawaban
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1. Jawaban ahreumlim
No. 18
Misal
u = 1 - 2x²
du = -4x dx
-du/4 = x dx
Jadi integral dapat ditulis
-3/4 ∫ √u du
= -3/4 (2/3) u^(3/2) + c
= (-1/2) u^(3/2) + c
= (-1/2) (1-2x²)^(3/2) + c ==> D
Nomor 19
Misal
u = sin x
du = cos x dx
Maka ∫ sin⁴x cos x dx
= ∫ u⁴ du
= u⁵/5 + c
= (1/5)sin⁵x + c ==> A
Nomor 20
Misal
u = x³ + 1
du = 3x² dx
du/3 = x² dx
Jangan lupa mengubah batas integral
u = x³ + 1
u = 1 + 1 = 2
u = 0 + 1 = 1
Maka ∫ 2x² (x³ + 1)⁵ dx {0...1}
= 2/3 ∫ u⁵ du { 1...2}
= 2/3 [u⁶/6] {1....2}
= 1/9 [u⁶] {2...1}
= 1/9 [2⁶ - 1⁶]
= 1/9 [64 - 1]
= 63/9
= 7