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Verifying Stoke’s Theorem In Exercises 3-6, verify Stoke’s Theorem by evaluating
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CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- Work by a constant force Evaluate a line integral to show thatthe work done in moving an object from point A to point B in thepresence of a constant force F = ⟨a, b, c⟩ is F ⋅ AB.arrow_forwardEvaluate the line integral using the Fundamental Theorem of Line Integrals. Use a computer algebra system to verify your results. (3yi + 3xj) · dr C: smooth curve from (0, 0) to (3, 7)arrow_forward人工知能を使用せず、すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 4. • (ex² + y²) dx + (ev² + x²)dy; C is the boundary of the triangle with vertices (0,0), (4,0) and (0,4)arrow_forward
- 人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT For Exercises 1-4, use Green's Theorem to evaluate the given line integral around the curve C, traversed counterclockwise. 3. J. 2ydx-3xdy; Cis the circle x2 + y2 = 1arrow_forwardQuestion 4 of 8 -/ 10 View Policies Current Attempt in Progress Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. $ 5 y'dx + 6x²dy, where Cis the square with vertices (0, 0), (2, 0), (2, 2), and (0, 2) oriented counterclockwise. fsy'dr + 6x'dy = i Attempts: 0 of 3 used Submit Answer Save for Later Using multiple attempts will impact your score. 30% score reduction after attempt 1arrow_forwardUsing the Fundamental Theorem of Line Integrals In Exercises 47-50, evaluate F· dr using the Fundamental Theorem of Line Integrals. F (x, y) = e²*i + e²»j C : line segment from (-1, –1) to (0,0)arrow_forward
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- Use Green's Theorem to evaluate the integral | x²ydx + xydy where C is the rectangle with vertices (0, 0), (3, 0), (3, 1) and (0, 1), oriented in the counterclockwise direction.arrow_forwardUse Green's Theorem to evaluate the following integral Let² dx + (5x + 9) dy Where C is the triangle with vertices (0,0), (11,0), and (10, 9) (in the positive direction).arrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT Compute the line integrals of the vector fields F. Graph the region of integration C F(x,y)=xyi- (x-2)j, C: y = x3 - 2x, from point (2,4) to point (1,-1)arrow_forward
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