parts a - c in pic A. State the Fundamental Theorem of Calculus for Line Integrals.grad f. Let C be the smooth curve withB. Suppose that f(x,y, z)parametric equations— ху + 2уz + 32x and F —x = 3t, y = 2t2, z = t°, 0

Part(A) FUNDAMENTAL THEOREM OF CALCULUS FOR LINE INTEGRALS: If we have a smooth curve C, given by…

A. State the Fundamental Theorem of Calculus for Line Integrals. B. Suppose that f(x, y, z) parametric equations = xy + 2yz + 3zx and F grad f. Let C be the smooth curve with = 3t, y = 2t², z = t³, 0

A. State the Fundamental Theorem of Calculus for Line Integrals. B. Suppose that f(x, y, z) parametric equations = xy + 2yz + 3zx and F grad f. Let C be the smooth curve with = 3t, y = 2t², z = t³, 0

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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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

Question

parts a - c in pic

A. State the Fundamental Theorem of Calculus for Line Integrals.
grad f. Let C be the smooth curve with
B. Suppose that f(x,y, z)
parametric equations
— ху + 2уz + 32x and F —
x = 3t, y = 2t2, z = t°, 0<t< 1.
(i) Find F = grad f and write it as F = Pi+Qj+Rk.
(ii) Compute the line integral of F along C, i.e.,
Pах + Qdy + Rdz.
C
You must compute the line integral directly by using the given parametrization.
C. Check your answer in part B by using the Fundamental Theorem of Calculus for Line Integrals.

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