Let F(x, y) = x² yi + x2j. Evaluate the line integral Sa F(r) · dr over the curve C parameterized by r(t) = t° i + t² j where t goes from -1 to 1. Round yo %3D answer to two decimal places.
Let F(x, y) = x² yi + x2j. Evaluate the line integral Sa F(r) · dr over the curve C parameterized by r(t) = t° i + t² j where t goes from -1 to 1. Round yo %3D answer to two decimal places.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \( \mathbf{F}(x, y) = x^2 y \, \mathbf{i} + x^2 \, \mathbf{j} \). Evaluate the line integral
\[
\int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}
\]
over the curve \( C \) parameterized by
\[
\mathbf{r}(t) = t^3 \, \mathbf{i} + t^2 \, \mathbf{j}
\]
where \( t \) goes from \(-1\) to \(1\). Round your answer to two decimal places.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d9747ea-4e67-4156-9289-0dc96263d473%2F6a215e44-e017-4a6a-958b-0267eb1bcd69%2F0bnil8i_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( \mathbf{F}(x, y) = x^2 y \, \mathbf{i} + x^2 \, \mathbf{j} \). Evaluate the line integral
\[
\int_C \mathbf{F}(\mathbf{r}) \cdot d\mathbf{r}
\]
over the curve \( C \) parameterized by
\[
\mathbf{r}(t) = t^3 \, \mathbf{i} + t^2 \, \mathbf{j}
\]
where \( t \) goes from \(-1\) to \(1\). Round your answer to two decimal places.
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