Nilai dari ∫19(5x−2x1−3)dx=…

Pertanyaan

Nilai dari $integral subscript 1 superscript 9 open parentheses 5 square root of x minus fraction numerator 1 over denominator 2 square root of x end fraction minus 3 close parentheses d x equals horizontal ellipsis$

Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Ingat

$integral x to the power of n space d x equals fraction numerator 1 over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus C$

sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell integral subscript 1 superscript 9 open parentheses 5 square root of x minus fraction numerator 1 over denominator 2 square root of x end fraction minus 3 close parentheses d x end cell equals cell integral subscript 1 superscript 9 open parentheses 5 x to the power of 1 half end exponent minus 1 half x to the power of negative 1 half end exponent minus 3 close parentheses space d x end cell row blank equals cell open square brackets 5 times 2 over 3 x square root of x minus square root of x minus 3 x close square brackets subscript 1 superscript 9 end cell row blank equals cell open square brackets 90 minus 3 minus 27 close square brackets minus open square brackets 10 over 3 minus 1 minus 3 close square brackets end cell row blank equals cell 60 plus 2 over 3 end cell row blank equals cell 60 2 over 3 end cell end table$