Pertanyaan

Nilai dari adalah ....

Nilai dari $begin mathsize 14px style integral subscript 1 superscript 4 space open parentheses 3 square root of x minus fraction numerator 1 over denominator square root of x end fraction close parentheses d x end style$ adalah ....

S. Intan

Master Teacher

Mahasiswa/Alumni Institut Pertanian Bogor

Jawaban terverifikasi

Pembahasan

$begin mathsize 14px style integral subscript 1 superscript 4 open parentheses 3 square root of straight x minus fraction numerator 1 over denominator square root of straight x end fraction close parentheses dx equals integral subscript 1 superscript 4 open parentheses 3 straight x to the power of 1 half end exponent minus straight x to the power of negative 1 half end exponent close parentheses dx equals open square brackets 3.2 over 3 straight x to the power of 3 over 2 end exponent minus 2 straight x to the power of 1 half end exponent close square brackets subscript 1 superscript 4 equals open square brackets 2 x to the power of 2 over 3 end exponent minus 2 x to the power of 1 half end exponent close square brackets subscript blank superscript blank equals open parentheses 2 open parentheses 4 close parentheses to the power of 3 over 2 end exponent minus 2 open parentheses 4 close parentheses to the power of 1 half end exponent close parentheses minus open parentheses 2 open parentheses 1 close parentheses to the power of 3 over 2 end exponent minus 2 open parentheses 1 close parentheses to the power of 1 half end exponent close parentheses equals left parenthesis 16 minus 4 right parenthesis minus left parenthesis 2 minus 2 right parenthesis equals 12 space end style$