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Evaluate the line integral, where
C is the given space curve.

int_(C)z^(2)dx+x^(2)dy+y^(2)dz,C is the line segment from
(1,0,0) to
(3,1,4)

Evaluate the line integral, where $C$ is the given space curve. $\newline$ $\int_{C} z^{2} d x+x^{2} d y+y^{2} d z, C$ is the line segment from $(1,0,0)$ to $(3,1,4)$

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Find derivatives of sine and cosine functions

Full solution

Q. Evaluate the line integral, where

C

is the given space curve.

\newline

\int_{C} z^{2} d x+x^{2} d y+y^{2} d z, C

is the line segment from

(1,0,0)

to

(3,1,4)

Determine Parameterization: Determine the parameterization of the curve $C$ from $(1,0,0)$ to $(3,1,4)$ .
Compute Derivatives: Compute the derivatives of the parameterized components.
Substitute and Compute: Substitute the parameterization into the integrand and compute $dx, dy, dz$ .
Simplify Integrand: Simplify the expression for the integrand.
Combine Like Terms: Combine like terms in the integrand.
Integrate Expression: Integrate the simplified expression from $t = 0$ to $t = 1$ .
Calculate Integral: Calculate the integral.

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