How long is this curve if you pulled it out straight? 📏 Swap it for short straight pieces. Each piece is the long side of a tiny right-angled triangle, so Pythagoras gives you its length. Add them all up, use the gradient to write each rise in terms of x, then shrink the pieces to nothing. The sum becomes an integral, and that's the arc length formula. #maths #calculus #alevelmaths #integration #mathstok
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How long is this curve if you pulled it out straight? 📏 Swap it for short straight pieces. Each piece is the long side of a tiny right-angled triangle, so Pythagoras gives you its length. Add them all up, use the gradient to write each rise in terms of x, then shrink the pieces to nothing. The sum becomes an integral, and that's the arc length formula. #maths #calculus #alevelmaths #integration #mathstok
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