Jika y=x21​, carilah dxdy​ kemudian tentukan nilai ∫x−21​dx dan ∫2x21​dx.

Pertanyaan

Jika , carilah  kemudian tentukan nilai  dan .

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F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Pembahasan

Jika

begin mathsize 14px style y equals x to the power of begin inline style 1 half end style end exponent fraction numerator d y over denominator d x end fraction equals 1 half x to the power of begin inline style 1 half end style minus 1 end exponent fraction numerator d y over denominator d x end fraction equals 1 half x to the power of negative begin inline style 1 half end style end exponent y apostrophe equals fraction numerator 1 over denominator 2 x to the power of 1 half end exponent end fraction space a t a u space fraction numerator 1 over denominator 2 square root of x end fraction end style 

Maka

begin mathsize 14px style integral fraction numerator 1 over denominator 2 x to the power of 1 half end exponent end fraction d x equals x to the power of begin inline style 1 half end style end exponent plus C integral fraction numerator 1 over denominator 2 x to the power of 1 half end exponent end fraction d x equals square root of x plus C integral x to the power of negative 1 half end exponent d x equals 2 integral fraction numerator 1 over denominator 2 x to the power of 1 half end exponent end fraction d x integral x to the power of negative 1 half end exponent d x equals 2 square root of x plus C end style

Dan

begin mathsize 14px style integral 2 x to the power of begin inline style 1 half end style end exponent d x equals 2 integral x to the power of begin inline style 1 half end style end exponent d x integral 2 x to the power of begin inline style 1 half end style end exponent d x equals open parentheses 2 times fraction numerator 1 over denominator 1 half plus 1 end fraction x to the power of begin inline style 1 half plus 1 end style end exponent close parentheses plus C integral 2 x to the power of begin inline style 1 half end style end exponent d x equals open parentheses 2 times fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction x to the power of begin inline style 3 over 2 end style end exponent close parentheses plus C integral 2 x to the power of begin inline style 1 half end style end exponent d x equals open parentheses 2 times fraction numerator 2 over denominator begin display style 3 end style end fraction x to the power of begin inline style 3 over 2 end style end exponent close parentheses plus C integral 2 x to the power of begin inline style 1 half end style end exponent d x equals 4 over 3 x to the power of begin inline style 3 over 2 end style end exponent plus C integral 2 x to the power of begin inline style 1 half end style end exponent d x equals fraction numerator 4 x over denominator 3 end fraction square root of x plus C end style  

 

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Meyvita Ryafintika Putri

Mudah dimengerti Pembahasan lengkap banget Ini yang aku cari! Makasih ❤️

Ridho Pratama

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Jika y=1−4x​, carilah nilai dxdy​ kemudian tentukan ∫1−4x​1​dx.

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