Math Problem Statement
To calculate the surface area of each function: (using f(x) as an example)
8.91151 f √1 + f (x) 2
SA π (x) dx 1 = 2 ∫ 0.38085
8.91151 2 0 + 1 √1 + ( (0.00430x .02196x .36528)) dxdy 2 0 + 1 2
SA π (0.00430x .02196x .36528) dx 1 = 2 ∫ 0.38085 = 74.11264 ≈ 74.1cm2
apply this to my polynomial function and for the surface area of a sphere. ∫ f(x) dx = −0.0111573898143 x12 + 0.1703013752625x11 −1.0531878972711x10 +3.1478135332496x9 − 3.0298776084592x8 − 9.6898781492810x7 + 40.2040231489677x6 − 68.9937226700263x5 +67.439770070160x4 − 39.0477196233909x3 +13.2768195135906x2 + 0.6362182975726x + C
Solution
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Math Problem Analysis
Mathematical Concepts
Integral Calculus
Surface Area Calculation
Polynomial Functions
Sphere Surface Area
Formulas
Surface area of revolution formula: $SA = 2\pi \int_a^b f(x) \sqrt{1 + \left( \frac{df}{dx} \right)^2} dx$
Sphere surface area formula: $SA = 4\pi r^2$
Theorems
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Suitable Grade Level
Advanced Mathematics
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