5π/4
∫ π * ( 0 - tan(x) )^2 dx ≈ 1.3
3π/4
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Using the Washer: <--- about x-axis
A(x) = π * ( x^3-4x^2+4x - 0 )^2 - π * ( x^4 - 0 )^2
A(x) = π * [ ( x^6 - 8x^5 + 24x^4 - 32x^3 + 16x^2 ) - x^8 ]
A(x) = π * ( x^6 - 8x^5 + 24x^4 - 32x^3 + 16x^2 - x^8 )
1
∫ π * ( x^6 - 8x^5 + 24x^4 - 32x^3 + 16x^2 - x^8 ) dx = 262π/315
0
about the line y = 2
Using the Washer: <--- about x-axis
A(x) = π * ( 2 - x^4 )^2 - π * ( 2 - ( x^3-4x^2+4x ) )^2
A(x) = π * ( ( 2 - x^4 )^2 - ( 2 - ( x^3-4x^2+4x ) )^2 )
1
∫ π * ( ( 2 - x^4 )^2 - ( 2 - ( x^3-4x^2+4x ) )^2 ) dx = 641π/315
0
about y-axis: Using the Shell Method:
1
∫ 2π * x * ( x^3-4x^2+4x - x^4 ) dx = 11π/15
0
about x = -2: Using the Shell Method:
1
∫ 2π * (x + 2) * ( x^3-4x^2+4x - x^4 ) dx = 18π/15
0
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