Question

(1 point) Evaluate $\iint_S \sqrt{1 + x^2 + y^2} \, dS$ where $S$ is the helicoid: \begin{align} \mathbf{r}(u, v) = u \cos(v)\mathbf{i} + u \sin(v)\mathbf{j} + v\mathbf{k}, \quad \text{with } 0 \le u \le 5, 0 \le v \le 3\pi \end{align}

          (1 point) Evaluate $\iint_S \sqrt{1 + x^2 + y^2} \, dS$ where $S$ is the helicoid: \begin{align*} \mathbf{r}(u, v) = u \cos(v)\mathbf{i} + u \sin(v)\mathbf{j} + v\mathbf{k}, \quad \text{with } 0 \le u \le 5, 0 \le v \le 3\pi \end{align*}

(1 point) Evaluate √(1 + x^2 + y^2) dS where S is the helicoid:
𝐫(u, v) = u cos(v)𝐢 + u sin(v)𝐣 + v𝐤, with 0 ≤ u ≤ 5, 0 ≤ v ≤ 3π

Added by Alexander B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

07/11/2023

Step 1

The helicoid is given by the parameterization r(u,v) = ucos(v)i + usin(v)j + vk, with 0 ≤ u ≤ 5 and 0 ≤ v ≤ 3π. Show more…

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(1 point) Evaluate ∬_(S)sqrt(1+x^(2)+y^(2))dS where S is the helicoid: r(u,v)=ucos(v)i+usin(v)j+vk, with 0<=u<=5,0<=v<=3pi (1 point) Evaluate V1 + 2 + y2 dS where S is the helicoid: r(u,v)=ucos(v)i+usin(u)j+vk,with0< u<5,0<v<3T