Pertanyaan

F ( x ) = 3 ∫ x d = f ( x ) + C dengan f ( x ) = 3 x , maka agar F ( 4 ) = 19 , nilai C = ...

$F (x) = 3 \int x d = f (x) + C$ dengan $f (x) = 3 x$ , maka agar $F (4) = 19$ , nilai $C = ...$

L. Marlina

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

nilai C = 3.

Pembahasan

Kita cari terlebih dahulu fungsi . Ingat Maka, Jadi, nilai C = 3.

Kita cari terlebih dahulu fungsi F open parentheses x close parentheses . Ingat

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

Maka,

$F open parentheses x close parentheses equals integral subscript blank superscript blank 3 square root of x d x space space space space space space space equals integral subscript blank superscript blank 3 x to the power of 1 half end exponent d x space space space space space space space equals fraction numerator 3 over denominator 3 over 2 end fraction. space x to the power of 3 over 2 end exponent plus C space space space space space space space equals 2 x square root of x plus C$

Jadi, nilai C = 3.