Pertanyaan

Tentukan hasil integral tak tentu berikut. ∫ x d x

Tentukan hasil integral tak tentu berikut.

$\int x d x$

H. Eka

Master Teacher

Mahasiswa/Alumni Universitas Pendidikan Indonesia

Jawaban terverifikasi

Jawaban

nilai dari

table attributes columnalign right center left columnspacing 0px end attributes row blank blank integral end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank space end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell text d end text end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell square root of x end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank c end table

Pembahasan

Rumus integral tak tentu: untuk sehingga Dengan demikian, nilai dari

Rumus integral tak tentu:

$integral space a x to the power of n space text d end text x equals fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c$ untuk n not equal to negative 1

sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral square root of x space text d end text x end cell equals cell integral space x to the power of 1 half end exponent space text d end text x end cell row blank equals cell fraction numerator 1 over denominator begin display style 1 half end style plus 1 end fraction x to the power of 1 half plus 1 end exponent plus c end cell row blank equals cell fraction numerator 1 over denominator begin display style 3 over 2 end style end fraction x to the power of 3 over 2 end exponent plus c end cell row blank equals cell 2 over 3 x to the power of 3 over 2 end exponent plus c end cell row blank equals cell 2 over 3 x square root of x plus c end cell end table$

Dengan demikian, nilai dari