Carilah hasil dari a. [tex] \int\limits^4_0 { \sqrt{x} } \, dx [/tex] b. [tex] \int\limits^3_1 ({5-x}) \, dx [/tex] c. [tex] \int\limits^8_0 ({ x^{2}-1)} \, dx
Matematika
han190
Pertanyaan
Carilah hasil dari
a. [tex] \int\limits^4_0 { \sqrt{x} } \, dx [/tex]
b. [tex] \int\limits^3_1 ({5-x}) \, dx [/tex]
c. [tex] \int\limits^8_0 ({ x^{2}-1)} \, dx [/tex]
d. [tex] \int\limits^b_a \frac{dx}{ x^{2}}[/tex]
a. [tex] \int\limits^4_0 { \sqrt{x} } \, dx [/tex]
b. [tex] \int\limits^3_1 ({5-x}) \, dx [/tex]
c. [tex] \int\limits^8_0 ({ x^{2}-1)} \, dx [/tex]
d. [tex] \int\limits^b_a \frac{dx}{ x^{2}}[/tex]
1 Jawaban
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1. Jawaban DB45
Integral tertentu
1.
₀⁴ ∫ √x dx = ₀⁴∫ x¹/² dx = ²/₃ [ x³/²]⁴₀
= 2/3 (4³/² - 0³/²)
= 2/3 ( 8)
= 16/3
2. ₁³∫ 5 - x dx = [5x - 1/2 x²}³₁
= 5(3-1) - 1/2(3²-1²)
= 5(2) - 1/2(9-1)
= 10 - 4
= 6
3. ₀⁸∫ x² - 1 dx = [1/3 x³ - x]⁸₀
= 1/3(8³-0³) - (3-0)
= 1/3(512) - 3
= (512 -9)/3 = 503/3 = 167 ²/₃
4.
ₐᵇ∫ dx/x² = ₐᵇ∫x⁻² dx = - [1/x]ᵇᵃ
= - (1/b - 1/a)
= - (a-b)/(ab)