Approximate the area between $h(x)$ and the $x$-axis from $x=-1$ to $x=1$ using a right Riemann sum with 4 equal subdivisions.
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R(4)=
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$\square$ units $^{2}$.

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Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To approximate the area between $h(x)$ and the $x$-axis from $x = -1$ to $x = 1$ using a right Riemann sum with 4 equal subdivisions, we first determine the width of each subdivision. The interval $[-1, 1]$ is divided into 4 equal parts, so each subdivision has a width of $\Delta x = \frac{1 - (-1)}{4} = \frac{2}{4} = 0.5$. ‖ ‖ step 2 ⋮ Next, we identify the right endpoints of each subdivision. These are $x = -0.5, 0, 0.5, 1$. ‖ ‖ step 3 ⋮ We then evaluate the function $h(x)$ at these right endpoints: $h(-0.5), h(0), h(0.5), h(1)$. ‖ ‖ step 4 ⋮ The right Riemann sum is given by the sum of the function values at these points, each multiplied by the width of the subdivisions: $$ R(4) = \Delta x \left( h(-0.5) + h(0) + h(0.5) + h(1) \right) $$ $$ R(4) = 0.5 \left( h(-0.5) + h(0) + h(0.5) + h(1) \right) $$ ‖ ‖ step 5 ⋮ Substitute the values of $h(x)$ at the right endpoints into the formula to get the final approximation. ‖ ∻Answer∻ ⚹ $R(4) = 0.5 \left( h(-0.5) + h(0) + h(0.5) + h(1) \right)$ units$^2$ ⚹ ∻Key Concept∻ ⚹Right Riemann Sum⚹ ∻Explanation∻ ⚹The right Riemann sum approximates the area under a curve by summing the areas of rectangles whose heights are determined by the function values at the right endpoints of each subdivision.⚹◊What is the formula for calculating the area between a function and the $x$-axis using a right Riemann sum with 4 equal subdivisions?⍭ Generate me a similar question◊

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