Pertanyaan

Hasil dari ∫ 4 1 − x 2 d x = ....

Hasil dari $\int \frac{1}{4} - x^{2} d x =$ ....

N. Rahayu

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah E.

Pembahasan

Ingat kembali integral berikut ini. Sehingga, Jadi, jawaban yang tepat adalah E.

Ingat kembali integral berikut ini.

$begin mathsize 14px style integral square root of a squared minus x squared end root blank d x equals fraction numerator a squared times x over a times fraction numerator square root of a squared minus x squared end root over denominator a end fraction plus a squared sin to the power of negative 1 end exponent invisible function application open parentheses x over a close parentheses over denominator 2 end fraction plus C end style$

Sehingga,

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

Jadi, jawaban yang tepat adalah E.