Find the area under the curve f(x) = e⁴^x over the interval [0, 5]. A) 121,291,300 B) 37 C) 20 D) 121,291,299 E) 485,165,195

Question

Quizplus · Accepted Answer

Using the power rule for integration, we have:

∫e^(x^2) dx = (1/2)√π erf(x) + C, where erf(x) is the error function.

Plugging in the limits of integration, we get:

∫₀^5 e^(x^2) dx = (1/2)√π (erf(5) - erf(0))

Using a calculator or a table of values for the error function, we find:

∫₀^5 e^(x^2) dx ≈ 1.21291299 x 10^8

The closest answer choice is D) 121,291,299.

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