Pertanyaan

Hasil dari ∫ 16 + x 2 d x = ....

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

A. Khairunisa

Master Teacher

Mahasiswa/Alumni Universitas Negeri Semarang

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

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

Ingat kembali integral berikut ini!

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

Maka diperoleh

$begin mathsize 14px style integral square root of 16 plus x squared end root blank d x equals integral square root of 4 squared plus x squared end root blank d x equals 4 squared open parentheses fraction numerator fraction numerator square root of 4 squared plus x squared end root over denominator 4 end fraction times x over 4 over denominator 2 end fraction plus fraction numerator ln invisible function application open vertical bar fraction numerator square root of 4 squared plus x squared end root over denominator 4 end fraction plus x over 4 close vertical bar over denominator 2 end fraction close parentheses plus C equals 16 times fraction numerator open parentheses x over 16 square root of 16 plus x squared end root plus ln invisible function application 1 fourth open vertical bar square root of 16 plus x squared end root plus x close vertical bar close parentheses over denominator 2 end fraction plus C equals 8 open parentheses x over 16 square root of 16 plus x squared end root plus ln invisible function application 1 fourth open vertical bar square root of 16 plus x squared end root plus x close vertical bar close parentheses plus C equals 1 half x square root of 16 plus x squared end root plus 8 ln invisible function application 1 fourth open vertical bar square root of 16 plus x squared end root plus x close vertical bar plus C end style$

Jadi, jawaban yang tepat adalah B.