Set Up an Integral for the Area of the Surface $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

question 69

Multiple Choice

Set up an integral for the area of the surface generated by revolving the given curve about the indicated axis.
- $$y = x ^ { 3 } , 0 \leq x \leq 2 ; x \text {-axis }$$

• A) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• B) \(\pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• C) \(\pi \int _ { 0 } ^ { 2 } x ^ { 3 } \sqrt { 1 + 9 x ^ { 4 } } d x\)
• D) \(2 \pi \int _ { 0 } ^ { 2 } x ^ { 2 } \sqrt { 1 + 9 x ^ { 4 } } d x\)

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