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### Section 7.3 : Trig Substitutions

For problems 1 – 8 use a trig substitution to eliminate the root.

1. $$\sqrt {4 - 9{z^2}}$$ Solution
2. $$\sqrt {13 + 25{x^2}}$$ Solution
3. $${\left( {7{t^2} - 3} \right)^{\frac{5}{2}}}$$ Solution
4. $$\sqrt {{{\left( {w + 3} \right)}^2} - 100}$$ Solution
5. $$\sqrt {4{{\left( {9t - 5} \right)}^2} + 1}$$ Solution
6. $$\sqrt {1 - 4z - 2{z^2}}$$ Solution
7. $${\left( {{x^2} - 8x + 21} \right)^{\frac{3}{2}}}$$ Solution
8. $$\sqrt {{{\bf{e}}^{8x}} - 9}$$ Solution

For problems 9 – 16 use a trig substitution to evaluate the given integral.

1. $$\displaystyle \int{{\frac{{\sqrt {{x^2} + 16} }}{{{x^4}}}\,dx}}$$ Solution
2. $$\displaystyle \int{{\sqrt {1 - 7{w^2}} \,dw}}$$ Solution
3. $$\displaystyle \int{{{t^3}{{\left( {3{t^2} - 4} \right)}^{\frac{5}{2}}}\,dt}}$$ Solution
4. $$\displaystyle \int_{{ - 7}}^{{ - 5}}{{\frac{2}{{{y^4}\sqrt {{y^2} - 25} }}\,dy}}$$ Solution
5. $$\displaystyle \int_{1}^{4}{{2{z^5}\sqrt {2 + 9{z^2}} \,dz}}$$ Solution
6. $$\displaystyle \int{{\frac{1}{{\sqrt {9{x^2} - 36x + 37} }}\,dx}}$$ Solution
7. $$\displaystyle \int{{\frac{{{{\left( {z + 3} \right)}^5}}}{{{{\left( {40 - 6z - {z^2}} \right)}^{\frac{3}{2}}}}}\,dz}}$$ Solution
8. $$\displaystyle \int{{\cos \left( x \right)\sqrt {9 + 25 \sin^2\left( x \right)} \,dx}}$$ Solution