Question

Determine \(\mathbf{r}(t)\) if \(\mathbf{r}'(t) = 1t^3 \mathbf{i} + 4\sqrt{t} \mathbf{j} + \frac{5}{t^2} \mathbf{k}\) and \(\mathbf{r}(1) = 5 \mathbf{i} + 1 \mathbf{j} + 4 \mathbf{k}\) \(\mathbf{r}(t) = \underline{\qquad} \mathbf{i} + \underline{\qquad} \mathbf{j} + \underline{\qquad} \mathbf{k}\) Submit Answer Tries 0/8 Evaluate the integral \(\int_0^1 \left( \frac{5}{1+t^2} \mathbf{i} + \frac{4t}{1+t^2} \mathbf{j} + (5 + 1t + 3t^2) \mathbf{k} \right) dt\) \(\underline{\qquad} \mathbf{i} + \underline{\qquad} \mathbf{j} + \underline{\qquad} \mathbf{k}\)

          Determine \(\mathbf{r}(t)\) if
\(\mathbf{r}'(t) = 1t^3 \mathbf{i} + 4\sqrt{t} \mathbf{j} + \frac{5}{t^2} \mathbf{k}\)
and
\(\mathbf{r}(1) = 5 \mathbf{i} + 1 \mathbf{j} + 4 \mathbf{k}\)
\(\mathbf{r}(t) = \underline{\qquad} \mathbf{i} + \underline{\qquad} \mathbf{j} + \underline{\qquad} \mathbf{k}\)
Submit Answer Tries 0/8
Evaluate the integral
\(\int_0^1 \left( \frac{5}{1+t^2} \mathbf{i} + \frac{4t}{1+t^2} \mathbf{j} + (5 + 1t + 3t^2) \mathbf{k} \right) dt\)
\(\underline{\qquad} \mathbf{i} + \underline{\qquad} \mathbf{j} + \underline{\qquad} \mathbf{k}\)

Determine 𝐫(t) if
𝐫'(t) = 1t^3 𝐢 + 4√(t)𝐣 + (5)/(t^2)𝐤
and
𝐫(1) = 5 𝐢 + 1 𝐣 + 4 𝐤
𝐫(t) = 𝐢 + 𝐣 + 𝐤
Submit Answer Tries 0/8
Evaluate the integral
∫0^1 ( (5)/(1+t^2)𝐢 + (4t)/(1+t^2)𝐣 + (5 + 1t + 3t^2) 𝐤) dt
𝐢 + 𝐣 + 𝐤

Added by Amy E.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Determine r(t) if r^(')(t)=1t^(3)i+4sqrt(t)j+(5)/(t^(2))k and r(1)=5i+1j+4k r(t)=,i+ k Tries( 0)/(8) Evaluate the integral int_0^1 ((5)/(1+t^(2))i+(4t)/(1+t^(2))j+(5+1t+3t^(2))k)dt i+,j+ Determine r(tif rt=1i+4j+ k t2 and r1-5i+1j+4k 71 i+ j+ k Submit Answer Tries 0/8 Evaluate the integral 5 4t i4 1+2 dt i+ k j+