Question

Find the area, if it is finite, of the region under the graph of y=12x⁵ ᵉ⁻ˣ6 over [0,[infinity]). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The area of the region is_____.

Answer 1

The area under the graph of y=12x⁵ ᵉ⁻ˣ6 over [0,[infinity]) is infinite.

Step-by-step explanation:

To find the area under the graph of y=12x⁵ ᵉ⁻ˣ6 over [0,[infinity]), we need to evaluate the integral of the function from 0 to infinity. The integral of 12x⁵ ᵉ⁻ˣ6 with respect to x can be calculated using the power rule and the exponential rule of integration. Integrating the function gives us:

Area = ∫0∞ 12x⁵ ᵉ⁻ˣ6 dx

Area = ∞

Therefore, the area under the graph is infinite.