Question

Q. siang
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Soal Intergral
[tex]∫x²(2-x³)½ \: dx \: adalah . . . .[/tex]
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Note : Wajib Memakai Cara
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Answer 1

Integral

∫x^n dx = 1/(n + 1) x^(n + 1) + C

y' = dy/dx → dx = dy /y'

∫x² (2 - x³)^1/2 dx

= ∫x² (2 - x³)^1/2 d(2 - x³) / (-3x²)

= -1/3 ∫(2 - x³)^1/2 d(2 - x³)

= -1/3 . 1/(1/2 + 1) . (2 - x³)^(1/2 + 1) + C

= -1/3 . 2/3 (2 - x³)^3/2 + C

= -2/9 (2 - x³)√(2 - x³) + C