Evaluate

∫
1
4
4
𝑥
3
𝑑
𝑥

Question

Evaluate

∫
1
4
4
𝑥
3
𝑑
𝑥

BlackTom AI · Accepted Answer

To begin, I interpret the expression as an integral with limits from 1 to 4 of the function 4x^3 with respect to x.
Next, I find an antiderivative: the antiderivative of x^3 is x^4/4, so multiplying by 4 gives 4*(x^4/4) = x^4.
Then I apply the Fundamental Theorem of Calculus by evaluating the antiderivative at the upper and lower bounds: x^4 | from x=1 to x=4 equals 4^4 − 1^4.
Compute the powers: 4^4 = 256 and 1^4 = 1, so the difference is 256 − 1 = 255.
Finally, I compare this with the given answer, noting that the computed value aligns with the provided numerical result. If formatting or interpretation were ambiguous, I would verify the integrand and limits again to ensure consistency with the problem statement.

Evaluate ∫ 1 4 4 𝑥 3 𝑑 𝑥

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