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Tentukan integral dari .

Pertanyaan

Tentukan integral dari integral open parentheses 2 x squared minus 3 x plus 1 close parentheses space straight d x.

Pembahasan Soal:

Gunakan konsep integral penjumlahan, pengurangan dan perkalian skalar dengan fungsi.

table attributes columnalign right center left columnspacing 2px end attributes row cell integral open square brackets f open parentheses x close parentheses plus g open parentheses x close parentheses close square brackets space straight d x end cell equals cell integral f open parentheses x close parentheses space straight d x plus integral g open parentheses x close parentheses space straight d x end cell row cell integral open square brackets f open parentheses x close parentheses minus g open parentheses x close parentheses close square brackets space straight d x end cell equals cell integral f open parentheses x close parentheses space straight d x minus integral g open parentheses x close parentheses space straight d x end cell row cell integral a x to the power of n straight d x end cell equals cell fraction numerator a over denominator n plus 1 end fraction x to the power of n plus 1 end exponent plus c end cell row cell integral a space straight d x end cell equals cell a x plus c end cell end table

Akan ditentukan integral dari integral open parentheses 2 x squared minus 3 x plus 1 close parentheses space straight d x.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell integral open parentheses 2 x squared minus 3 x plus 1 close parentheses space straight d x end cell equals cell integral 2 x squared space straight d x minus integral 3 x space straight d x plus integral 1 space straight d x end cell row blank equals cell fraction numerator 2 over denominator 2 plus 1 end fraction x to the power of 2 plus 1 end exponent minus fraction numerator 3 over denominator 1 plus 1 end fraction x to the power of 1 plus 1 end exponent plus 1 times x plus c end cell row blank equals cell 2 over 3 x cubed minus 3 over 2 x squared plus x plus c end cell end table

Jadi, diperoleh hasil integral dari integral open parentheses 2 x squared minus 3 x plus 1 close parentheses space straight d x adalah 2 over 3 x cubed minus 3 over 2 x squared plus x plus c.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 20 Juli 2021

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