## \begin{aligned} \text { work } &=\int \mathbf{F} . \mathbf{T} d s \\ &=\int_{C} \mathbf{F} \cdot \frac{d \mathbf{r}}{d x} d x \end{aligned}$$\begin{array}{c}{=k \int_{a}^{b} \frac{d}{d x}\left(\sqrt{x^{2}+[f(x)]^{2}}\right) d x} \\ {=k\left(\sqrt{x^{2}+[f(x)]^{2}}\right)_{a}^{b}}\end{array}$$$$\begin{array}{l}{=k\left(\sqrt{b^{2}+[f(b)]^{2}}-\sqrt{a^{2}+[f(a)]^{2}}\right)} \\ {=k\left[\left(b^{2}+(f(b))^{2}\right)^{\frac{1}{2}}-\left(a^{2}+(f(a))^{2}\right)^{2}\right]} \\ {\text { Hence, proved. }}\end{array}$$

Vector Calculus

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in this question to given that are equals x oy los y g. So let's say we'll be equal X oy los therefore eggs G so you are or the eggs will be equally I plus if Bess X she and also it's given that f equals key. Well, what route? X square. Last voice. Where not deploy eggs. I plus why is G, which is has constant magnitude key and points away from the origin? Who so if multiplying the are over, the X will be equal que x or fruit X squared los y square plus G. Why it will dash with X work route X squared plus y is good, which will be equal que eggs plus okay if X if off national banks Oh, what route Exit Square plus April Fix all the schools if recently find we can get key the over the eggs square root X square, plus if off eggs. But we're still now. By using change rules, we can get the integration off f Multiply t R over the X as integration from our boundaries A and B de de over p x or multiply square root excess square, plus if off eggs force to the X, which will be equal key. The place where route Thanks a square Los F X squared with our boundaries e and B. So now if we succeed cue ball, our our boundaries, we can get key. Don't apply square root. He square los if off B it's wound minus square root. He squared plus a full e squid. Ask them. Did the question?

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Vector Calculus

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