Question

10. Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y) = \langle x^3 - y, x + y^3 \rangle$ and $C$ the boundary of the region enclosed by $y = x^2$ and $y = x$, directed clockwise. 11. Use a line integral to find the area of the region bounded by the ellipse $4x^2 + y^2 = 4.$

          10. Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y) = \langle x^3 - y, x + y^3 \rangle$ and $C$ the boundary of the region enclosed by $y = x^2$ and $y = x$, directed clockwise.
11. Use a line integral to find the area of the region bounded by the ellipse $4x^2 + y^2 = 4.$

10. Evaluate 𝐅· d𝐫 where 𝐅(x, y) = ⟨ x^3 - y, x + y^3 ⟩ and C the boundary of the region enclosed by y = x^2 and y = x, directed clockwise.
11. Use a line integral to find the area of the region bounded by the ellipse 4x^2 + y^2 = 4.

Added by Alicia P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/06/2023

Step 1

We can parameterize this as $\mathbf{r}_1(t) = \langle t, t^2 \rangle$, $0 \le t \le 1$. * $C_2$: $y = x$, $1 \le x \le 0$. We can parameterize this as $\mathbf{r}_2(t) = \langle t, t \rangle$, $1 \le t \le 0$. Show more…

Show all steps

Thanks for your feedback!

10. Evaluate $\int_C \mathbf{F} \cdot d\mathbf{r}$ where $\mathbf{F}(x, y) = \langle x^3 - y, x + y^3 \rangle$ and $C$ the boundary of the region enclosed by $y = x^2$ and $y = x$, directed clockwise. 11. Use a line integral to find the area of the region bounded by the ellipse $4x^2 + y^2 = 4$.