Pertanyaan

Nilai dari ∫ 1 2 2 x 2 5 x 2 − 2 x 2 3 d x = ...

Nilai dari $\int_{1}^{2} \frac{5 x ^{2}}{2 x ^{2}} - \frac{3}{2 x ^{2}} d x = ...$ $\;$

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Jawaban

.

$integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x equals 1 3 over 4$ .

Pembahasan

Ingat! dengan adalah konstanta. Jadi, .

Ingat!

dengan adalah konstanta.

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction space d x minus integral subscript 1 superscript 2 fraction numerator 3 over denominator 2 x squared end fraction space d x end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell integral subscript 1 superscript 2 5 over 2 space d x minus 3 over 2 integral subscript 1 superscript 2 x to the power of negative 2 end exponent space d x end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets fraction numerator 1 over denominator 0 plus 1 end fraction x to the power of 0 plus 1 end exponent close square brackets subscript 1 superscript 2 minus 3 over 2 open square brackets fraction numerator 1 over denominator negative 2 plus 1 end fraction x to the power of negative 2 plus 1 end exponent close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets x close square brackets subscript 1 superscript 2 minus 3 over 2 open square brackets negative x to the power of negative 1 end exponent close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 open square brackets x close square brackets subscript 1 superscript 2 plus 3 over 2 open square brackets 1 over x close square brackets subscript 1 superscript 2 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 left parenthesis 2 minus 1 right parenthesis plus 3 over 2 open parentheses 1 half minus 1 over 1 close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 left parenthesis 1 right parenthesis plus 3 over 2 open parentheses fraction numerator 1 minus 2 over denominator 2 end fraction close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 plus 3 over 2 open parentheses negative 1 half close parentheses end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 5 over 2 minus 3 over 4 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell fraction numerator 5 left parenthesis 2 right parenthesis minus 3 over denominator 4 end fraction end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell fraction numerator 10 minus 3 over denominator 4 end fraction end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 7 over 4 end cell row cell integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x end cell equals cell 1 3 over 4 end cell end table$

Jadi, $integral subscript 1 superscript 2 fraction numerator 5 x squared over denominator 2 x squared end fraction minus fraction numerator 3 over denominator 2 x squared end fraction space d x equals 1 3 over 4$ .