Jawaban Soal Ujian Matematika IPA Kelas 12 no 29 Tahun 2016

Soal Ujian Matematika IPA Kelas 12

Tahun 2016

Soal Pilihan Ganda

29. Hasil dari ∫ x (1-2x)³dx = ...

A. -1/40 (1 + 8x) (1 - 2x)⁴ + c
B. -1/80 (1 + 8x) (1 - 2x)⁴ + c
C. 1/80 (1 - 8x) (1 - 2x)⁴ + c
D. 1/80 (1 + 8x) (1 - 2x)⁴ + c
E. 1/40 (1 - 8x) (1 - 2x)⁴ + c

Jawaban : B

U = 1 - 2x
dU = -2 dx
dx = -1/2 dU

U = 1 - 2x
2x = 1 - U
x = 1/2 - 1/2U

∫ x (1-2x)³dx
= ∫ (1/2 - 1/2U) (U)³. (-1/2 dU)
= ∫ (1/2U³ - 1/2U⁴) . (-1/2 dU)
= ∫ - (1/4U³ - 1/4U⁴) dU
= -1/16 U⁴ + 1/20 U⁵ + c
= -1/16 (1 - 2x)⁴ + 1/20 (1 - 2x)⁵+ c

= -1/16 (1 - 2x)⁴ + 1/20 (1 - 2x)(1 - 2x)⁴+ c

= -1/16 (1 - 2x)⁴ + (1/20 - 1/10x)(1 - 2x)⁴+ c

= (-1/16 + (1/20 - 1/10x))(1 - 2x)⁴+ c
= (- 5/80 + 4/80 - 1/10x)(1 - 2x)⁴+ c

= (-1/80 - 1/10x)(1 - 2x)⁴+ c

= -1/80 (1 + 8x)(1 - 2x)⁴+ c

>>>Soal No.30