dtl42 said:
The formula for integrating sqrt(x^2+1)/x^2 using trig is: ∫(sqrt(x^2+1)/x^2)dx = ln|x+sqrt(x^2+1)|+C.
Trigonometry is used because it provides a way to simplify the expression sqrt(x^2+1)/x^2 into a more manageable form. By using trigonometric identities, we can rewrite the expression as a combination of trigonometric functions, which can then be integrated using standard techniques.
The domain of sqrt(x^2+1)/x^2 is all real numbers except for x=0, as dividing by 0 is undefined. This means that the integral can be evaluated for any value of x except 0.
Yes, the integral can be evaluated using substitution. By substituting u = x+sqrt(x^2+1), we can rewrite the integrand as 1/u and use the rule for integrating 1/u to find the solution.
Yes, there is a geometric interpretation of the integral. The integral represents the area under the curve of the function sqrt(x^2+1)/x^2 from x=0 to x=∞. This can be visualized as the area of an infinite triangle with base x and height sqrt(x^2+1), which is equal to ln|x+sqrt(x^2+1)|+C.