Jawab:

Penjelasan dengan langkah-langkah:

volume putar sumbu x

v =π ₐᵇ∫ (y₁²- y₂²) dx

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v  putar kurva  dan  garis

kurva y =9- x² diatas garis y = x + 7

i) batas integral

x+ 7 = 9 - x²

x² + x - 2 = 0

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

x= - 2  ataux = 1

batas bawah (a) = -2  , batas atas (b) = 1

V= π ₋₂¹∫ (9- x²)²- (x + 7)² dx

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

V = π ₋₂¹∫(  x⁴- 19x² - 14x + 32)dx

V = π [  ¹/₅ x⁵ - ¹⁹/₃ x³ - 7x² +32x]¹₋₂

V=  π [ ¹/₅ (1+ 32) - ¹⁹/₃ (1 + 8) - 7(1- 4) +32(1 + 2)]

V=  π [ ³³/₅ -  57 + 21 + 96 ]

V = 66³/₅ π