Question

Tolong bantu jawab soal di gambar ya
isi caranya juga
makasi

Answer 1

Gris melalui (1,0),(0,1) -->x+y = 1 -->y= 1 - x
kurva  y = 2x²

tik potong  garis dan kurva
2x² = 1- x
2x² +x - 1 =  0
(2x-1)(x+1) = 0
x = 1/2  atau x = -1
x= 1/2, y = 1/2

 mengelilingi sumbu y
batas intergral y = 0 sd y = 1/2
x+y = 1 --> x  = 1- y
y = 2x² --> x² = 1/2 y

V = π  ₀¹/² ∫ (1-y)² -(1/2 y) dy
V = π ₀ ¹/²∫ 1- 2y + y² - 1/2 y dy
V = π ₀ ¹/² ∫ y² - ⁵/₂ y + 1 dy

V = π [ ¹/₃ y³ - ⁵/₄ y² + y ]¹/² ₀

V = π [ ¹/₃(¹/₈) - ⁵/₄(¹/₄) + (¹/₂)]
V = π [¹/₂₄ - ⁵/₁₆+ ¹/₂]
V = π [¹¹/₄₈]