The discussion centers on the challenges of using substitution to evaluate the integral 0∫2 sqrt(4-x^2). While a direct substitution such as u=x^2 fails due to the absence of the necessary factor (2x), a trigonometric substitution, specifically x = 2cos(θ), is effective. Participants clarify that substitution can work, but the choice of substitution is critical for successful integration. The conversation emphasizes the importance of selecting appropriate substitutions in integral calculus.
PREREQUISITESStudents of calculus, mathematics educators, and anyone seeking to deepen their understanding of integration techniques, particularly in the context of trigonometric substitutions.
schapman22 said:Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.
schapman22 said:Why doesn't substitution work to find 0∫2 sqrt(4-x^2). I kn ow you can find the integral in other ways. I am just curious why regular substitution won't work. Thank you in advance.