Exercise
$\frac{2\pi}{\sqrt{2}}\int_{1}^{2}\left(x^{2}+2x^{2}-1\right)^{\frac{1}{2}}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral (2pi)/(2^(1/2))int((x^2+2x^2+-1)^(1/2))dx&1&2. Combining like terms x^2 and 2x^2. First, factor the terms inside the radical by 3 for an easier handling. Taking the constant out of the radical. We can solve the integral \frac{2\pi }{\sqrt{2}}\int\sqrt{3}\sqrt{x^2-\frac{1}{3}}dx by applying integration method of trigonometric substitution using the substitution.
Find the integral (2pi)/(2^(1/2))int((x^2+2x^2+-1)^(1/2))dx&1&2
Final answer to the exercise
$\frac{7.6609568\pi }{2.4494898}+0.313481\pi +\frac{-0.1570581\pi }{2.4494898}$