Pertanyaan

Jika y = x 2 1 , carilah d x d y kemudian tentukan nilai ∫ x − 2 1 d x dan ∫ 2 x 2 1 d x .

Jika $y = x^{\frac{1}{2}}$ , carilah $\frac{d y}{d x}$ kemudian tentukan nilai $\int x^{- \frac{1}{2}} d x$ dan $\int 2 x^{\frac{1}{2}} d x$ .

F. Ayudhita

Master Teacher

Jawaban terverifikasi

Pembahasan

Jika Maka Dan

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

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