2 \pi \int_{ 0 }^{ 1 }\left( x^{ 3 }\sqrt{ 1 + ( 3x^{ 2 } ) ^{ 2 } } \right) d x

asked by guest
on Apr 01, 2025 at 11:06 am



You asked:

Evaluate the expression: 2π⋅∫01x31+(3x2)2dx2 \pi \cdot \int_{0}^{1}{{x}^{3} \sqrt{1 + {\left( 3 {x}^{2} \right)}^{2}}}dx

MathBot Answer:

Evaluated



2π⋅∫01x31+(3x2)2dx=2π(−154+51027)\displaystyle 2 \pi \cdot \int_{0}^{1}{{x}^{3} \sqrt{1 + {\left( 3 {x}^{2} \right)}^{2}}}dx = 2 \pi \left(- \frac{1}{54} + \frac{5 \sqrt{10}}{27}\right)

Expanded

2π⋅∫01x31+(3x2)2dx=2π∫01x39x4+1 dx2 \pi \cdot \int_{0}^{1}{{x}^{3} \sqrt{1 + {\left( 3 {x}^{2} \right)}^{2}}}dx = 2 \pi \int\limits_{0}^{1} x^{3} \sqrt{9 x^{4} + 1}\, dx

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