Pertanyaan

Jika y = 1 − 4 x , carilah nilai d x d y kemudian tentukan ∫ 1 − 4 x 1 d x .

Jika $y = 1 - 4 x$ , carilah nilai $\frac{d y}{d x}$ kemudian tentukan $\int \frac{1}{1 - 4 x} d x$ .

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Jika Maka

Jika

$begin mathsize 14px style y equals square root of 1 minus 4 x end root y equals open parentheses 1 minus 4 x close parentheses to the power of bevelled 1 half end exponent m i s a l blank u equals 1 minus 4 x m a k a blank fraction numerator d u over denominator d x end fraction equals negative 4 y equals blank u to the power of bevelled 1 half end exponent m a k a blank fraction numerator d y over denominator d u end fraction equals 1 half u to the power of bevelled fraction numerator negative 1 over denominator 2 end fraction end exponent s e h i n g g a y apostrophe equals fraction numerator d y over denominator d x end fraction fraction numerator d y over denominator d x end fraction equals fraction numerator d y over denominator d u end fraction bullet blank fraction numerator d u over denominator d x end fraction y apostrophe equals 1 half u to the power of bevelled fraction numerator negative 1 over denominator 2 end fraction end exponent bullet left parenthesis negative 4 right parenthesis y to the power of apostrophe equals negative 2 u to the power of bevelled fraction numerator negative 1 over denominator 2 end fraction end exponent y to the power of apostrophe equals negative fraction numerator 2 over denominator square root of u end fraction y to the power of apostrophe equals negative fraction numerator 2 over denominator square root of 1 minus 4 x end root end fraction end style$

Maka

$begin mathsize 14px style integral negative fraction numerator 2 over denominator square root of 1 minus 4 x end root end fraction d x equals square root of 1 minus 4 x end root plus C integral fraction numerator 1 over denominator square root of 1 minus 4 x end root end fraction d x equals negative 1 half integral negative fraction numerator 2 over denominator square root of 1 minus 4 x end root end fraction d x integral fraction numerator 1 over denominator square root of 1 minus 4 x end root end fraction d x equals negative 1 half open parentheses square root of 1 minus 4 x end root close parentheses plus C integral fraction numerator 1 over denominator square root of 1 minus 4 x end root end fraction d x equals negative fraction numerator square root of 1 minus 4 x end root over denominator 2 end fraction plus C end style$