Question

Persiapan UN, banyak yang lupa? latihan yoook bersama BRAINLY.

y = x², dan y = 4x - 3, diputar mengelilingi sumbu x dengan 360 derajat, berapa volume benda putar tersebut

Answer 1

Cari batas

y = y

x² = 4x - 3

x² - 4x + 3 = 0

(x - 3) (x - 1) = 0

x = 3 ✅ x = 1

V = π ₁∫³ {y₁² - y₂²} dx

V = π ₁∫³ {[x²]² - [4x - 3]²} dx

V = π ₁∫³ {x⁴ - [16x² - 24x + 9]} dx

V = π ₁∫³ {x⁴ - 16x² + 24x - 9} dx

V = π ₁|³ [x⁵/5 - 16x³/3 + 12x² - 9x]

V = π {[3⁵/5 - 16•3³/3 +12•3² - 9•3] - [1⁵/5 - 16•1³/3 + 12•1² - 9•1]}

V = π {[243/5 - 144 + 108 - 27] - [1/5 - 16/3 + 12 - 9]}

V = π {[-14,4] - [-2,13]}

V = π {[-14,4 + 2,13]}

V = π {[-12,27]}

V = 12,27π ✔