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Pertanyaan

∫ 0 1 ​ ln x d x

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A. Rahmawati

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

adalah .

 integral subscript 0 superscript 1 ln space x d x adalah x space ln space open vertical bar x close vertical bar space minus 1 space plus C.

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Pembahasan

Jadi, adalah .

integral subscript 0 superscript 1 ln space x d x

 

table attributes columnalign right center left columnspacing 0px end attributes row cell misal comma space straight u space end cell equals cell space ln vertical line straight x vertical line space end cell row cell du space end cell equals cell space 1 divided by straight x space dx space space end cell row cell dv space end cell equals cell space dx space end cell row cell straight v space end cell equals cell space straight x space space end cell row blank equals cell space uv space minus space integral subscript 0 superscript 1 straight v space du space end cell row blank equals cell space ln vertical line straight x vertical line. straight x space minus space integral subscript 0 superscript 1 straight x space open parentheses 1 over straight x close parentheses space dx space end cell row blank equals cell space straight x. ln vertical line straight x vertical line space minus space integral subscript 0 superscript 1 dx space end cell row blank equals cell space straight x. ln vertical line straight x vertical line space minus space space large x subscript 0 superscript 1 plus space straight C space end cell row blank equals cell space space straight x. ln vertical line straight x vertical line minus 1 plus space straight C end cell end table

Jadi, integral subscript 0 superscript 1 ln space x d x adalah x space ln space open vertical bar x close vertical bar space minus 1 space plus C.

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