Evaluate \int_c xdx+zdy-ydz

Question:

Evaluate {eq}\displaystyle \int xdx+ydy-zdz {/eq}

Integration:

Integration is the sum under the curve under defined limits which is given by:

{eq}\iiint f(x,y,z)dxdydz {/eq}

Answer and Explanation:

{eq}\int_c xdx+zdy-ydz\\ \text{Using Linearlity for integration}\\ \int(a f(x)+b g(x)) d x=a \int f(x) d x+b \int g(x) d x \int \:xdx+\int \:ydy-\int \:zdz\\ =\frac{x^2}{2}+C+\frac{y^2}{2}+C-\left(\frac{z^2}{2}+C\right)\\ =\frac{-z^2+x^2+y^2}{2}+C\\ {/eq}


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Integration Problems in Calculus: Solutions & Examples

from AP Calculus AB & BC: Homework Help Resource

Chapter 13 / Lesson 13
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