[+50] - Universityku

penyelesaian nya ↓
$sfint(20 {x}^{4} + 10 {x}^{4} + 20 {x}^{3} + 6 {x}^{2} - 4 {x}^{2} )dx \$

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[+50]

Jawaban:

Rumus:

$sf : int {ax}^{n} : dx = frac{a}{n + 1} {x}^{n + 1} + c \$

$:$

$sfint(20 {x}^{4} + 10 {x}^{4} + 20 {x}^{3} + 6 {x}^{2} - 4 {x}^{2} )dx \$

$sf = frac{20}{4 + 1} {x}^{4 + 1} + frac{10}{4 + 1} {x}^{4 + 1} + frac{20}{3 + 1} {x}^{3 + 1} + frac{6}{2 +1 } {x}^{2 + 1} - frac{4}{2 + 1} {x}^{2 + 1}$

$sf = frac{20}{5} {x}^{5} + frac{10}{5} {x}^{5} + frac{20}{4} {x}^{4} + frac{6}{3} {x}^{3} - frac{4}{3} {x}^{3}$

$sf = 4 {x}^{5} + 2 {x}^{5} + {5x}^{4} + frac{6 - 4}{3} {x}^{3}$

$sf = 6 {x}^{5} +5 {x}^{4} + frac{2}{3} {x}^{3} + c$

Penjelasan dengan langkah-langkah:

Integral :

(20x⁴ + 10x⁴ + 20x³ + 6x² – 4x²)dx

fx^ndx = 1 / n + 1 x^n+1 + c

Int 20x⁴ = 1 / 4 + 1 x^4+1

= 1/5x^5

= 20.1/5x^5

= 20/5x^5

= 4x^5

Int 10x⁴ = 1/4+1x^4+1

= 1/5x^5

= 10/5x^5

= 2x^5

Int 20x³ = 1/3+1x^3+1

= 1/4x^4

= 20/4x⁴

= 5x⁴

Int 6x² = 1/2+1x^2+1

= 1/3x^3

= 6.1/3x^3

= 6/3x^3

= 2x³

Int -4x² = 1/2+1x^2+1

= 1/3x³

= -4.1/3x³

= -4/3x³

Jadi 4x^5 + 2x^5 + 5x⁴ + 2x³ – 4/3x³ + c

= 6x^5 + 5x⁴ + 2x³ – 4/3x³ + c

= 6x^5 + 5x⁴ + 2/3x³ + c