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Hitung. 3 . ∫ 2 − 5 x 2 ​ d x ​

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S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

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Pembahasan

Diperoleh intergalnya yaitu: Ingatlah bahwa: Kemudian diperoleh: Maka,hasil integral dari adalah .

Diperoleh intergalnya yaitu:

table attributes columnalign right center left columnspacing 0px end attributes row cell integral fraction numerator d x over denominator square root of 2 minus 5 x squared end root end fraction end cell equals cell integral fraction numerator 1 over denominator square root of 5 open parentheses begin display style 2 over 5 end style minus x squared close parentheses end root end fraction d x end cell row blank equals cell integral fraction numerator 1 over denominator square root of 5 times square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator 1 over denominator square root of 5 end fraction times fraction numerator square root of 5 over denominator square root of 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell end table

Ingatlah bahwa:

integral fraction numerator 1 over denominator a squared minus x squared end fraction d x equals arcsin times x over a

Kemudian diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator square root of 5 over denominator 5 end fraction integral fraction numerator 1 over denominator square root of begin display style 2 over 5 end style minus x squared end root end fraction d x end cell equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x over denominator square root of begin display style 2 over 5 end style end root end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x over denominator begin display style fraction numerator square root of 2 over denominator square root of 5 end fraction end style end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times x times fraction numerator square root of 5 over denominator square root of 2 end fraction plus C end cell row blank equals cell fraction numerator square root of 5 over denominator 5 end fraction times arcsin times fraction numerator x square root of 5 over denominator square root of 2 end fraction times fraction numerator square root of 2 over denominator square root of 2 end fraction plus C end cell row blank equals cell fraction numerator square root of 5 space arcsin space begin display style fraction numerator straight x square root of 10 over denominator 2 end fraction end style over denominator 5 end fraction plus C end cell end table

Maka, hasil integral dari integral fraction numerator d x over denominator square root of 2 minus 5 x squared end root end fraction adalah fraction numerator square root of 5 space arcsin space begin display style fraction numerator x square root of 10 over denominator 2 end fraction end style over denominator 5 end fraction plus C.

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