Question

QUIZ (1376)
Materi: Integral

Tentukan hasil integral terhadap x dari [tex] f(x)= \dfrac{ a }{ b }x^{n-1} [/tex] dengan a, b bilangan real, b ≠ 0, dan n rasional!​

Answer 1

Jawab:
[tex]\displaystyle\rm =\frac{ax^{n}}{bn} +C[/tex]

Penjelasan:
[tex]\displaystyle\rm f(x) =\frac{ax^{n-1}}{b}\\\\Ditanya\:\:\:integralnya\\\\\int \:\frac{ax^{n-1}}{b}\:dx\\\\=\frac{1}{b}\:\int \:ax^{n-1} dx\\\\=\frac{1}{b}\:\left(\frac{ax^{n-1+1}}{n-1+1}\right)\\\\=\frac{1}{b}\:\left(\frac{ax^{n}}{n}\right)\\\\=\frac{ax^{n}}{bn} +C[/tex]

(xcvi)

Answer 2

Verified answer

Jawaban:

[tex] \displaystyle \int \dfrac{a}{b} {x}^{n - 1}\:dx = \bold{\dfrac{{ax}^{n}}{bn} }+ C [/tex]

Penjelasan dengan langkah-langkah:

[tex]f(x) = \dfrac{a}{b} {x}^{n - 1} [/tex]

[tex] \to\displaystyle \int \dfrac{a}{b} {x}^{n - 1}\:dx [/tex]

[tex] \displaystyle\dfrac{a}{b} \int \frac{1}{ 1}{x}^{n - 1}\:dx [/tex]

[tex] \displaystyle = \frac{a}{b}\times \frac{\frac{1}{1}}{ n - 1 + 1}{x}^{n - 1+1} +C [/tex]

[tex] \displaystyle = \frac{a}{b} \times\frac{ {x}^{n} }{n} + C[/tex]

[tex] = \bold{\dfrac{{ax}^{n}}{bn} }+ C[/tex]