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Jika ∫−10​f(x)dx =−12 dan ∫01​f(x) dx =15 maka nilai ∫−11​f(x) dxadalah...

Pertanyaan

Jika integral subscript negative 1 end subscript superscript 0 f left parenthesis x right parenthesis d x space equals negative 12 dan integral subscript 0 superscript 1 f left parenthesis x right parenthesis space d x space equals 15

maka nilai integral subscript negative 1 end subscript superscript 1 f left parenthesis x right parenthesis space d xadalah...

  1. -27

  2. -3

  3. 0

  4. 3

  5. 27

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

gunakan aturan integral berikut ini:

integral subscript a superscript b f left parenthesis x right parenthesis d x equals F left parenthesis x right parenthesis left enclose blank with a below and b on top equals F left parenthesis b right parenthesis minus F left parenthesis a right parenthesis end enclose

diketahui:

integral subscript negative 1 end subscript superscript 0 f left parenthesis x right parenthesis d x equals negative 12 space d a n integral subscript 0 superscript 1 f left parenthesis x right parenthesis equals 15  m a k a comma  integral subscript negative 1 end subscript superscript 0 f left parenthesis x right parenthesis d x equals 12  F left parenthesis 0 right parenthesis minus space F left parenthesis negative 1 right parenthesis equals 12 space... left parenthesis 1 right parenthesis    d a n  integral subscript 0 superscript 1 f left parenthesis x right parenthesis equals 15  F left parenthesis 1 right parenthesis minus space F left parenthesis 0 right parenthesis space equals 15 space.... left parenthesis 2 right parenthesis

sehingga jika kita eliminasi persamaan (1) dan persamaan (2) diperoleh:

bottom enclose blank with negative F left parenthesis 0 right parenthesis plus F left parenthesis 1 right parenthesis equals 15 space space plus below and F left parenthesis 0 right parenthesis minus F left parenthesis negative 1 right parenthesis equals space 12 on top end enclose  F left parenthesis 1 right parenthesis minus F left parenthesis negative 1 right parenthesis space equals 27    space m a k a space  integral subscript negative 1 end subscript superscript 1 f left parenthesis x right parenthesis d x space equals space F left parenthesis 1 right parenthesis minus F left parenthesis negative 1 right parenthesis  equals 27

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