Hasil dari ∫(x−3)(x+3)dx=...

Pertanyaan

Hasil dari $\style{font-size:14px}{\int\left(\sqrt x-3\right)\left(\sqrt x+3\right)\operatorname dx=...}$

N. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Padang

Jawaban terverifikasi

Jawaban

hasil dari

adalah

Pembahasan

Perhatikan perhitungan berikut.

Ingat:

$begin mathsize 14px style integral x to the power of n d x equals fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C integral a d x equals a x plus C end style$

Maka:

$begin mathsize 12px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses square root of x minus 3 close parentheses open parentheses square root of x plus 3 close parentheses d x end cell equals cell integral open parentheses square root of x close parentheses open parentheses square root of x close parentheses plus 3 square root of x minus 3 square root of x plus open parentheses negative 3 close parentheses open parentheses 3 close parentheses d x end cell row blank equals cell integral x minus 9 d x end cell row blank equals cell fraction numerator 1 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent minus 9 x plus C end cell row blank equals cell 1 half x squared minus 9 x plus C end cell end table end style$

Jadi, hasil dari adalah .