Jawab:

Penjelasan dengan langkah-langkah:

integrl

V putar sb x

y₁ = 9 - x²

y₂ = x +  7

i) batas integral

y₂ =  y₁

x + 7 = 9 - x²

x²+ x - 2= 0

( x+ 2)(x - 1) =0

x= - 2  atau x = 1

batas  bawah = a = - 2

batas atas = b = 1

ii. rumus volume kurva diatas garis

V = π ₐᵇ∫(y₁)² - (y₂)²  dx

V = π ₋₂¹∫(9 - x²)² - (x+ 7)²  dx

V = π ₋₂¹∫(81 - 18x² + x⁴ - (x² +14x+ 49)  dx

V = π ₋₂¹∫(81 - 18x² + x⁴ - x² - 14x - 49)  dx

V = π ₋₂¹∫( x⁴ -  19 x² + 32) dx

V = π [ ¹/₅ x⁵ -  ¹⁹/₃ x³ + 32 x]¹₋₂

V = π [ ¹/₅(1+32) -  ¹⁹/₃(1+8)+ 32 (1 +2) ]

V = π [ ³³/₅-  57 + 96 ]

V = 45³/₅ π satuan