Penjelasan dengan langkah-langkah:
[tex] \binom{3}{1} x {}^{2} (x + 3) + \binom{5}{3} x {}^{2} (x + 3)[/tex]
[tex] \binom{3}{1} {x}^{3} + 3 {x}^{2} + \binom{5}{3} { {x}^{3} } + 3 {x}^{2} [/tex]
[tex] |\frac{1}{4} {x}^{4} + {x}^{2} | \binom{3}{1} + | \frac{1}{4} {x}^{4} + {x}^{2} | \binom{5}{3} [/tex]
=[(¼.81+3/2.9)-(9)] + [(¼.625+3/2.25)-(¼.81+(9)]
=[81/4 + 54/4)-(9)]+[(625/4 + 150/4)-(81/4+54/4)]
= 1120/4
= 280
integral
∫f(x) dx [b a] + ∫f(x) dx [c b] = ∫f(x) dx [c a]
•
∫x²(x + 3) dx [3 1] + ∫x²(x + 3) [5 3]
= ∫(x³ + 3x²) dx [5 1]
= 1/4 x⁴ + x³
= 1/4 . 5⁴ + 5³ - (1/4 . 1³ + 1³)
= 625/4 + 125 - 5/4
= 620/4 + 125
= 155 + 125
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Penjelasan dengan langkah-langkah:
[tex] \binom{3}{1} x {}^{2} (x + 3) + \binom{5}{3} x {}^{2} (x + 3)[/tex]
[tex] \binom{3}{1} {x}^{3} + 3 {x}^{2} + \binom{5}{3} { {x}^{3} } + 3 {x}^{2} [/tex]
[tex] |\frac{1}{4} {x}^{4} + {x}^{2} | \binom{3}{1} + | \frac{1}{4} {x}^{4} + {x}^{2} | \binom{5}{3} [/tex]
=[(¼.81+3/2.9)-(9)] + [(¼.625+3/2.25)-(¼.81+(9)]
=[81/4 + 54/4)-(9)]+[(625/4 + 150/4)-(81/4+54/4)]
= 1120/4
= 280
Verified answer
integral
∫f(x) dx [b a] + ∫f(x) dx [c b] = ∫f(x) dx [c a]
•
∫x²(x + 3) dx [3 1] + ∫x²(x + 3) [5 3]
= ∫(x³ + 3x²) dx [5 1]
= 1/4 x⁴ + x³
= 1/4 . 5⁴ + 5³ - (1/4 . 1³ + 1³)
= 625/4 + 125 - 5/4
= 620/4 + 125
= 155 + 125
= 280