Pertanyaan

Hasil dari ∫ x 2 − 16 d x = ....

Hasil dari $\int x^{2} - 16 d x =$ ....

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Ingat kembali integral berikut ini! Maka diperoleh Jadi, jawaban yang tepat adalah C.

Ingat kembali integral berikut ini!

$begin mathsize 14px style integral square root of x squared minus a squared end root blank d x equals a squared open parentheses fraction numerator x over a square root of fraction numerator x squared minus a squared over denominator a end fraction end root over denominator 2 end fraction minus fraction numerator ln invisible function application open vertical bar x over a plus square root of fraction numerator x squared minus a squared over denominator a end fraction end root close vertical bar over denominator 2 end fraction close parentheses plus C end style$

Maka diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral square root of x squared minus 16 end root blank d x end cell equals cell integral square root of x squared minus 4 squared end root blank d x end cell row blank equals cell 4 squared open parentheses fraction numerator x over 4 times fraction numerator square root of x squared minus 4 squared end root over denominator 4 end fraction over denominator 2 end fraction minus fraction numerator ln invisible function application open vertical bar x over 4 plus fraction numerator square root of x squared minus 4 squared end root over denominator 4 end fraction close vertical bar over denominator 2 end fraction close parentheses plus C end cell row blank equals cell 16 times fraction numerator open parentheses x over 16 square root of x squared minus 16 end root minus ln invisible function application open vertical bar x over 4 plus 1 fourth square root of x squared minus 16 end root close vertical bar close parentheses over denominator 2 end fraction plus C end cell row blank equals cell 8 open parentheses x over 16 square root of x squared minus 16 end root minus ln invisible function application open vertical bar x over 4 plus 1 fourth square root of x squared minus 16 end root close vertical bar close parentheses plus C end cell row blank equals cell 1 half x square root of x squared minus 16 end root minus 8 ln invisible function application 1 fourth open vertical bar x plus square root of x squared minus 16 end root close vertical bar plus C end cell row blank blank blank end table end style$

Jadi, jawaban yang tepat adalah C.