Question

evaluate using trigonometric substitution. (use symbolic notation and fractions where needed. use for the arbitrary constant. absorb into as muсh as possible.) ∫(252 4)2=

Answer 1

To evaluate the integral using trigonometric substitution, use the substitution x = 4sin(theta) and follow the step-by-step instructions provided.

Step-by-step explanation:

To evaluate the integral using trigonometric substitution, we need to identify the appropriate substitution. In this case, we can use the substitution x = 4sin(theta), which allows us to express the integrand in terms of trigonometric functions. Here are the step-by-step instructions:

1. Substitute x = 4sin(theta) into the integral.
2. Express dx in terms of d(theta) using the derivative of sin(theta).
3. Express the integrand in terms of theta using the trigonometric identities.
4. Evaluate the integral using the new variable theta.
5. Substitute back x = 4sin(theta) to obtain the final result.

Following these steps will allow you to evaluate the integral using trigonometric substitution.