find the volume of the solid formed by revolving the region in quadrant 1 bounded by the y=(16-x^2)^1/2
the axais and the y axis about the y aixis
evaluate
S2xcosx dx
the axais and the y axis about the y aixis
evaluate
S2xcosx dx
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V = ∫ πx² dy
y = √(16 - x²) <==> x² = 16 - y²
y(0) = 4
V = ∫ πx² dy
V = ∫ π(16 - y²) dy = 16π - ⅓ y³ from y = 0 to y = 4
V = 128π / 3
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∫ 2xCosx dx
use ∫udv = uv - ∫vdu
u = 2x, <==> du = 2 dx
dv = Cosx, <==> v = Sinx
∫udv = uv - ∫vdu
∫2xCosx dx
= 2xSinx - ∫2Sinx dx
= 2xSinx + 2Cosx + C
= 2 (xSinx + Cosx) + C
y = √(16 - x²) <==> x² = 16 - y²
y(0) = 4
V = ∫ πx² dy
V = ∫ π(16 - y²) dy = 16π - ⅓ y³ from y = 0 to y = 4
V = 128π / 3
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∫ 2xCosx dx
use ∫udv = uv - ∫vdu
u = 2x, <==> du = 2 dx
dv = Cosx, <==> v = Sinx
∫udv = uv - ∫vdu
∫2xCosx dx
= 2xSinx - ∫2Sinx dx
= 2xSinx + 2Cosx + C
= 2 (xSinx + Cosx) + C