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**1. Homework Statement**

Integrate: [tex]\int[/tex][tex]\sqrt{1-9t^{2}}[/tex]dt

**2. Homework Equations**

**3. The Attempt at a Solution**

t = 1/3 sin[tex]\Theta[/tex]

dt/d[tex]\Theta[/tex] = 1/3 cos[tex]\Theta[/tex]

dt = 1/3 cos[tex]\Theta[/tex]d[tex]\Theta[/tex]

3t = sin[tex]\Theta[/tex]

1/3[tex]\int\sqrt{1-sin^{2}}\Theta[/tex] cos[tex]\Theta[/tex]d[tex]\Theta[/tex]

1/3[tex]\int cos^{2}\Theta[/tex]d[tex]\Theta[/tex]

1/3[tex]\int[/tex](1 + cos 2[tex]\Theta[/tex]) / 2 d[tex]\Theta[/tex]

1/6[tex]\int1 + cos2\Theta[/tex] d[tex]\Theta[/tex]

1/6([tex]\Theta + 1/2 sin 2\Theta[/tex]) + C

1/6([tex]\Theta + 1/2(sin\Theta cos\Theta[/tex]) + C

1/6([tex]\Theta + 1/2(sin\Theta\sqrt{1-sin^{2}\Theta}[/tex])) + C

1/6([tex]\Theta[/tex] + 1/2(3t[tex]\sqrt{1-9t^{2}}[/tex])) + C

I can't figure out how to get rid of [tex]\Theta[/tex] in the result.