Question

For integral using trigonometric substitution, you should:

A) Substitute a trigonometric function for x
B) Use partial fraction decomposition
C) Apply the power rule
D) Use u-substitution

Answer 1

For integrals involving trigonometric substitution, the correct option is A) Substitute a trigonometric function for x. Trigonometric substitution is a technique used to simplify integrals involving algebraic expressions using trigonometric functions. The correct answer is option is A .

Step-by-step explanation:

For integrals involving trigonometric substitution, the correct option is A) Substitute a trigonometric function for x. Trigonometric substitution is a technique used to simplify integrals involving algebraic expressions using trigonometric functions. It involves replacing the variable of integration with a trigonometric function and using trigonometric identities to simplify the integral.

Here is a step-by-step explanation:

1. Identify the integral expression that requires trigonometric substitution.
2. Let's say the integral is ∫f(x)dx. Choose a substitution that will eliminate the algebraic expression in the integral and replace it with a trigonometric function.
3. Make the appropriate substitution by letting x = g(t), where g(t) is the trigonometric function chosen.
4. Differentiate both sides of the substitution equation with respect to t and solve for dx in terms of dt.
5. Substitute the new variable and its derivative into the original integral, replacing x and dx.
6. Simplify the integral using trigonometric identities.
7. Perform any necessary algebraic operations to evaluate the integral.