Let $\mathbf{F}(x, y, z) = (3x^2 \ln(8y^2 + 5) + 7z^{10})\mathbf{i} + \left(\frac{16yx^3}{8y^2 + 5} + 3z\right)\mathbf{j} + (70xz^9 + 3y - 7\pi \sin \pi z)\mathbf{k}$ and let $\mathbf{r}(t) = (t^3 + 1)\mathbf{i} + (t^2 + 2)\mathbf{j} + t^3\mathbf{k}$, $0 \le t \le 1$. Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$.
Added by Edwin A.
Close
Step 1
dr, we need to find the dot product of F and dr. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 56 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The general anti-derivative(Integral) Example: Compute the general anti-derivative of the following functions
Adi S.
(a) evaluate $f(1,2)$ and $f(1.05,2.1)$ and calculate $\Delta z$, and (b) use the total differential $d z$ to approximate $\Delta z$ $$ f(x, y)=3 x-4 y $$
Functions of Several Variables
Differentials
Let F(x, y, z) = (3z + 2y, 5z + 2x, 5y + 3x) 1) Find a function f such that f(0, 0, 0) = 0 and F = ∇f. 2) Suppose C is any curve from (0, 0, 0) to (1, 2, 3). Evaluate ∧_c F ∙ dr.
Madhur L.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD