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

Question

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To compute the integral of $g(x) = 5x^4 - x^2 + 8$ from $x = 0$ to $x = 3$, we start by finding the antiderivative of the function. ‖ ‖ step 2 ⋮ The antiderivative of $5x^4$ is $\frac{5x^5}{5} = x^5$. ‖ ‖ step 3 ⋮ The antiderivative of $-x^2$ is $-\frac{x^3}{3}$. ‖ ‖ step 4 ⋮ The antiderivative of $8$ is $8x$. ‖ ‖ step 5 ⋮ Combining these, the antiderivative of $g(x)$ is $x^5 - \frac{x^3}{3} + 8x + C$. ‖ ‖ step 6 ⋮ We now evaluate this antiderivative from $0$ to $3$: ‖ ‖ step 7 ⋮ $ \left[ x^5 - \frac{x^3}{3} + 8x \right]_0^3 = \left( 3^5 - \frac{3^3}{3} + 8 \cdot 3 \right) - \left( 0^5 - \frac{0^3}{3} + 8 \cdot 0 \right) $. ‖ ‖ step 8 ⋮ Simplifying, we get $ \left( 243 - 9 + 24 \right) - 0 = 258 $. ‖ ∻Answer∻ ⚹ 258 ⚹ ∻Key Concept∻ ⚹Definite Integral⚹ ∻Explanation∻ ⚹The definite integral of a function over an interval is found by evaluating the antiderivative at the endpoints of the interval and subtracting.⚹◊What is the definite integral of the function $5x^4 - x^2 + 8$ from $x = 0$ to $x = 3$⍭ Generate me a similar question◊

Sia