Pertanyaan

Tentukan integral-integral berikut ini. ∫ ( 2 x 3 − 3 x 2 + 4 x − 5 ) d x

Tentukan integral-integral berikut ini.

$\int (2 x^{3} - 3 x^{2} + 4 x - 5) d x$

L. Indah

Master Teacher

Mahasiswa/Alumni Universitas Siliwangi

Jawaban terverifikasi

Jawaban

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Pembahasan

Dengan menggunakan sifat integral tak tentu diperoleh Dengan demikian, nilai dari

Dengan menggunakan sifat integral tak tentu $begin mathsize 14px style integral x to the power of n space straight d x equals fraction numerator x to the power of n plus 1 end exponent over denominator n plus 1 end fraction plus C space dan space integral a space straight d x equals a x plus C end style$ diperoleh

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell integral left parenthesis 2 x cubed minus 3 x squared plus 4 x minus 5 right parenthesis straight d x end cell equals cell fraction numerator 2 x to the power of 3 plus 1 end exponent over denominator 3 plus 1 end fraction minus fraction numerator 3 x to the power of 2 plus 1 end exponent over denominator 2 plus 1 end fraction plus fraction numerator 4 x to the power of 1 plus 1 end exponent over denominator 1 plus 1 end fraction minus 5 x plus C end cell row blank equals cell fraction numerator 2 x to the power of 4 over denominator 4 end fraction minus fraction numerator 3 x cubed over denominator 3 end fraction plus fraction numerator 4 x squared over denominator 2 end fraction minus 5 x plus C end cell row blank equals cell x to the power of 4 over 2 minus x cubed plus 2 x squared minus 5 x plus C end cell end table end style$

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