Rumus Integral Tak Tentu untuk $$x^n$$

Rumus integral tak tentu untuk $$x^n$$ (n ≠ -1) adalah $$\text{∫} x^n \text{dx} = \frac{x^{n+1}}{n+1} + C$$ .

Contoh Integral Tak Tentu: $$\text{∫} (6x^2 + 10x - 7) \text{dx}$$

$$\text{∫} (6x^2 + 10x - 7) \text{dx} = 2x^3 + 5x^2 - 7x + C$$ .

Contoh Integral Tak Tentu: $$\text{∫} (8x^3 - 3x^2 + x + 5) \text{dx}$$

$$\text{∫} (8x^3 - 3x^2 + x + 5) \text{dx} = 2x^4 - x^3 + \frac{1}{2}x^2 + 5x + C$$ .

Contoh Integral Tentu: $$\text{∫}_{2}^{3} (6x^2 - 2x + 7) \text{dx}$$

Hasil dari $$\text{∫}_{2}^{3} (6x^2 - 2x + 7) \text{dx} = 40$$ .

Contoh Integral Tentu: $$\text{∫}_{1}^{4} (3x^2) \text{dx}$$

$$\text{∫}_{1}^{4} (3x^2) \text{dx} = [x^3]_{1}^{4} = 64 - 1 = 63$$ .

Rumus Integral untuk Fungsi Polinomial

Rumus integral untuk fungsi polinomial adalah $$\text{∫} (ax^n) \text{dx} = \frac{a}{n+1} x^{n+1} + C$$ .

Contoh Integral Tak Tentu: $$\text{∫} x^2 \text{dx}$$

$$\text{∫} x^2 \text{dx} = \frac{1}{3}x^3 + C$$ .

Contoh Integral Tak Tentu: $$\text{∫} (9x^2 - 4x + 5) \text{dx}$$

$$\text{∫} (9x^2 - 4x + 5) \text{dx} = 3x^3 - 2x^2 + 5x + C$$ .

Pengertian Konstanta Integrasi

Konstanta integrasi ( $$C$$ ) adalah nilai yang ditambahkan pada hasil integral tak tentu untuk menunjukkan bahwa ada banyak fungsi yang memiliki turunan yang sama.

Contoh Soal Integral Tak Tentu dengan Pilihan Ganda

Soal: $$\text{∫} (6x^2 + 10x - 7) \text{dx}$$ . Pilihan: A) $$2x^3 + 5x^2 - 7x + C$$ , B) $$3x^2 + 5x - 7 + C$$ , C) $$2x^3 + 5x^2 - 7 + C$$ , D) $$2x^3 + 10x - 7 + C$$ . Jawaban: A.

Contoh Soal Integral Tentu dengan Pilihan Ganda

Soal: $$\text{∫}_{2}^{3} (6x^2 - 2x + 7) \text{dx}$$ . Pilihan: A) 32, B) 34, C) 36, D) 38, E) 40. Jawaban: E.

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Definisi Integral Tentu

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