Question

Describe the area represented by the definite integral ∫ (0,3) 2x^3 dx

Answer 1

Answer on Question #48164 – Math – Integral Calculus

Describe the area represented by the definite integral $\int_0^3 2x^3 dx$ .

Solution

This integral represents the area below the curve $y = 2x^3$ . The value of the integral above is

$$\int_ {0} ^ {3} 2 x ^ {3} d x = \int_ {0} ^ {3} 2 d \left(\frac {x ^ {4}}{4}\right) = 2 \left(\frac {x ^ {4}}{4}\right) _ {0} ^ {3} = \frac {3 ^ {4}}{2} = 40.5.$$

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