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Tentukan integral-integral berikut ini.

Tentukan integral-integral berikut ini.

begin mathsize 14px style integral left parenthesis 2 x cubed minus 3 x squared plus 4 x minus 5 right parenthesis space straight d x end style   undefined 

  1. ... undefined 

  2. ... undefined 

Jawaban:

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 

Jadi, nilai dari begin mathsize 14px style integral left parenthesis 2 x cubed minus 3 x squared plus 4 x minus 5 right parenthesis straight d x equals x to the power of 4 over 2 minus x cubed plus 2 x squared minus 5 x plus C end style 

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