If-c-is-the-line-segement-from-0-0-0-to-1-2-3-find-x-e-yz-ds-

Question Number 50689 by Tawa1 last updated on 18/Dec/18

If c is the line segement from (0, 0, 0) to (1, 2, 3)

find \int x e^{yz} ds

Answered by mr W last updated on 19/Dec/18

\frac{x - 1}{1} = \frac{y - 2}{2} = \frac{z - 3}{3}

\Rightarrow y = 2 x

\Rightarrow z = 3 x

d s = \sqrt{{(d x)}^{2} + {(d y)}^{2} + {(d z)}^{2}} = \sqrt{1 + 2^{2} + 3^{2}} d x = \sqrt{14} d x

\int {x e}^{y z} d s = \int_{0}^{1} {x e}^{6 x^{2}} \sqrt{14} d x

= \frac{\sqrt{14}}{12} \int_{0}^{1} e^{6 x^{2}} d (6 x^{2})

= \frac{\sqrt{14}}{12} {[e^{6 x^{2}}]}_{0}^{1}

= \frac{\sqrt{14}}{12} (e^{6} - 1)

Commented by Tawa1 last updated on 19/Dec/18

God bless you sir

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