Jika y=(3x+1)4, carilah nilai dxdy​ kemudian tentukan∫(3x+1)3dx.

Pertanyaan

Jika , carilah nilai  kemudian tentukan.   

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F. Ayudhita

Master Teacher

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Pembahasan

Pembahasan

Jika

begin mathsize 14px style y equals open parentheses 3 x plus 1 close parentheses to the power of 4 m i s a l u equals 3 x plus 1 fraction numerator d u over denominator d x end fraction equals 3 s e h i n g g a y equals u to the power of 4 fraction numerator d y over denominator d u end fraction equals 4 u cubed 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 times fraction numerator d u over denominator d x end fraction y apostrophe equals 4 u cubed times 3 y apostrophe equals 12 u cubed y apostrophe equals 12 left parenthesis 3 x plus 1 right parenthesis cubed end style 

Maka

begin mathsize 14px style integral 12 open parentheses 3 x plus 1 close parentheses cubed d x equals open parentheses 3 x plus 1 close parentheses to the power of 4 plus C integral open parentheses 3 x plus 1 close parentheses cubed d x equals 1 over 12 integral 12 open parentheses 3 x plus 1 close parentheses cubed d x integral open parentheses 3 x plus 1 close parentheses cubed d x equals 1 over 12 open parentheses 3 x plus 1 close parentheses to the power of 4 plus C integral open parentheses 3 x plus 1 close parentheses cubed d x equals open parentheses 3 x plus 1 close parentheses to the power of 4 over 12 plus C end style  

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Jika y=x8, carilah dxdy​ kemudian tentukan ∫x7dx dan ∫2x7dx.

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