Compute the integral of $g(x) = 5x^4 - x^2 + 8$ from $x = 0$ to $x = 3$.

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∻Solution by Steps∻ ‖ step 1 ⋮ We need to compute the integral of the function $g(x) = 5x^4 - x^2 + 8$ from $x = 0$ to $x = 3$. ‖ ‖ step 2 ⋮ The integral can be expressed as $\int_0^3 (5x^4 - x^2 + 8) \, dx$. ‖ ‖ step 3 ⋮ Evaluating the integral, we find: $\int (5x^4) \, dx = x^5$, $\int (-x^2) \, dx = -\frac{x^3}{3}$, and $\int 8 \, dx = 8x$. Thus, the antiderivative is $x^5 - \frac{x^3}{3} + 8x + C$. ‖ ‖ step 4 ⋮ Now, we evaluate this from 0 to 3: $[3^5 - \frac{3^3}{3} + 8(3)] - [0 - 0 + 0] = 243 - 9 + 24 = 258$. ‖ ∻Answer∻ ⚹ 258 ⚹ ∻Key Concept∻ ⚹ The Fundamental Theorem of Calculus allows us to evaluate definite integrals by finding the antiderivative of the function. ⚹ ∻Explanation∻ ⚹ The integral of the polynomial function was computed by finding its antiderivative and then evaluating it at the bounds of integration, resulting in a final value of 258. ⚹◊What is the antiderivative of $g(x) = 5x^4 - x^2 + 8$?⍭ Generate me a similar question◊

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