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Pertanyaan

∫ x x 2 − x ​ ​ d x = ...

 

  1. x squared plus 2 square root of x plus C 

  2. 1 half x squared plus 2 square root of x plus C 

  3. 1 half x squared minus 2 square root of x plus C 

  4. 1 half x squared plus x square root of x plus C 

  5. 1 half x squared minus x square root of x plus C 

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L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

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Pembahasan

Ingat, Ktia sederhanakan terlebih dahulu integrannya. Ingat maka Jadi, jawaban yang tepat adalah C.

Ingat, 

integral a x to the power of n space d x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C comma space space space n not equal to negative 1 

Ktia sederhanakan terlebih dahulu integrannya. Ingat 

a to the power of n over a to the power of m equals a to the power of n minus m end exponent space space space space space comma space space space square root of a equals a to the power of 1 half end exponent 

maka

 integral fraction numerator x squared minus square root of x over denominator x end fraction space d x equals integral x minus x to the power of negative begin inline style 1 half end style end exponent space d x space space space space space space space space space space space space space space space space space space space space space space space equals 1 half x squared minus fraction numerator 1 over denominator 1 half end fraction x to the power of begin inline style 1 half end style end exponent plus C space space space space space space space space space space space space space space space space space space space space space space space equals 1 half x squared minus 2 square root of x plus C

Jadi, jawaban yang tepat adalah C.

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