MTH $252$ Recitation Activity $3-$Winter $2025$

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The following questions are review for section $1\mathrm{.}1.$

$(6)$ Compute the indicated right Riemann sum $R_4$ for the function $f(x)=x^2$ on $-4,-2$

$(7)$ Use sigma notation to express the right Riemann sum with $n=100$ rectangles for $ln(x)$ on $1,e.$

$(8)$ The velocity of a horse traveling along a straight country lane is modeled by the function $v(t)=-(\frac{1}{15}t-\frac{2}{3}{)}^4+\frac{16}{81},$ where $v(t)$ is given in miles per minute and t is given in minutes. Use a right endpoint approximation with $n=4$ subintervals to approximate the total distance the horse travels in the first $15$ minutes. Write the specific Riemann sum and then use the Riemann sum calculator to compute a final answer. Include the correct units with your final answer.