Pertanyaan

∫ 1 4 5 x 2 − 6 x + x 2 2 d x

$\int_{1}^{4} 5 x^{2} - 6 x + \frac{2}{x ^{2}} d x$

O. Rahmawati

Master Teacher

Mahasiswa/Alumni UIN Sunan Gunung Djati Bandung

Jawaban terverifikasi

Pembahasan

ingat!

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript straight a superscript straight b mx to the power of straight n space dx end cell equals cell fraction numerator straight m over denominator straight n plus 1 end fraction straight x to the power of straight n plus 1 end exponent vertical line subscript straight a superscript straight b end cell row blank equals cell fraction numerator straight m over denominator straight n plus 1 end fraction straight b to the power of straight n plus 1 end exponent minus fraction numerator straight m over denominator straight n plus 1 end fraction straight a to the power of straight n plus 1 end exponent end cell end table$

$table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell integral subscript 1 superscript 4 5 x squared minus 6 square root of x plus 2 over x squared d x end cell row blank equals cell integral subscript 1 superscript 4 5 x squared minus 6 x to the power of 1 half end exponent plus 2 x to the power of negative 2 end exponent space d x end cell row blank equals cell open square brackets 5 over 3 x cubed minus fraction numerator 6 over denominator begin display style 3 over 2 end style end fraction x to the power of 3 over 2 end exponent plus fraction numerator 2 over denominator negative 1 end fraction x to the power of negative 1 end exponent close square brackets subscript 1 superscript 4 end cell row blank equals cell open square brackets 5 over 3 left parenthesis 4 right parenthesis cubed minus 4 left parenthesis 4 right parenthesis to the power of 3 over 2 end exponent minus 2 left parenthesis 4 right parenthesis to the power of negative 1 end exponent close square brackets minus open square brackets 5 over 3 left parenthesis 1 right parenthesis cubed minus 4 left parenthesis 1 right parenthesis to the power of 3 over 2 end exponent minus 2 left parenthesis 1 right parenthesis to the power of negative 1 end exponent close square brackets end cell row blank equals cell open square brackets 445 over 6 close square brackets minus open square brackets negative 13 over 3 close square brackets end cell row blank equals cell 157 over 2 end cell end table$