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Pertanyaan

Tentukan integral-integral tak tentu berikut ini.

d) begin mathsize 14px style integral open parentheses square root of x cubed end root minus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style 

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

nilai dari begin mathsize 14px style integral open parentheses square root of x cubed end root minus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style adalah begin mathsize 14px style 2 over 5 square root of x open parentheses x squared minus 10 close parentheses plus C end style.

Pembahasan

Integral tak tentu merupakan sebuah bentuk operas pengintegralan pada suatu fungsi menghasilkan suatu fungsi baru.

Nilai dari begin mathsize 14px style integral open parentheses square root of x cubed end root minus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral open parentheses square root of x cubed end root minus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end cell equals cell integral square root of x cubed end root space straight d x minus integral fraction numerator 2 over denominator square root of x end fraction space straight d x end cell row blank equals cell integral x to the power of begin inline style 3 over 2 end style end exponent space straight d x minus integral 2 x to the power of negative begin inline style 1 half end style end exponent space straight d x end cell row blank equals cell 2 over 5 x to the power of begin inline style 3 over 2 end style plus 1 end exponent plus C minus 2 open parentheses 2 x to the power of negative begin inline style 1 half end style plus 1 end exponent plus C close parentheses end cell row blank equals cell 2 over 5 x to the power of begin inline style 5 over 2 end style end exponent minus 4 x to the power of begin inline style 1 half end style end exponent plus C end cell row blank equals cell 2 over 5 x squared square root of x minus 4 square root of x plus C end cell row blank equals cell 2 over 5 square root of x open parentheses x squared minus 10 close parentheses plus C end cell end table end style        

Jadi, nilai dari begin mathsize 14px style integral open parentheses square root of x cubed end root minus fraction numerator 2 over denominator square root of x end fraction close parentheses straight d x end style adalah begin mathsize 14px style 2 over 5 square root of x open parentheses x squared minus 10 close parentheses plus C end style.

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