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*Find the exact length of the curve*$0 \le x \le 1$

\(\displaystyle y = 1 + 6x^{\frac{3}{2}}\) <-- If you can't read this, the exponent is \(\displaystyle \frac{3}{2}\)

\(\displaystyle

\therefore y' = 9\sqrt{x}\)

\(\displaystyle \int ^1_0 \sqrt{1 + (9\sqrt{x})^2} \, dx\)

\(\displaystyle = \int ^1_0 \sqrt{1 + 81x} \, dx\)

\(\displaystyle

= \int^1_0 1 + 9\sqrt{x} \, dx\)

Now can't I just split the two integrals separately to obtain:

\(\displaystyle x + 6x^{\frac{3}{2}} |^1_0 \) <-- If you can't read this, the exponent is \(\displaystyle \frac{3}{2}\)

Thus getting: \(\displaystyle 1 + 6 = 7? \)

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