Question

For x real, which substitution directly simplifies the radical in the expression below?

$$\frac{1}{\sqrt{49+x^{2}}}$$

Accepted Answer

$$\begin{aligned}&	ext{set }x=7	an(	heta),\;-\frac{\pi}{2}<	heta<\frac{\pi}{2}\ &dx=7\sec^{2}(	heta)\,d	heta\end{aligned}$$

Answer

$$\begin{aligned}	ext{set }x=7	an(	heta)	ext{, but take }dx=7\sec(	heta)\,d	heta\end{aligned}$$

Answer

$$\begin{aligned}	ext{set }x=7\sec(	heta),\;0<	heta<\frac{\pi}{2}	ext{, for the sum of squares}\end{aligned}$$

Answer

$$\begin{aligned}	ext{set }x=7\sin(	heta),\;-\frac{\pi}{2}<	heta<\frac{\pi}{2}	ext{, for the sum of squares}\end{aligned}$$

Practice: Integration - Trigonometric Substitution Method