Trigonometric Substitution Involving a Definite Integral: Part One (9.5.2)

Question 1

• Use trigonometric substitution to evaluate integrals involving the square root of the sum or difference of two squares.

1. Match the square root expression with the sides of a right triangle.
2. Substitute the corresponding trigonometric function into the integrand.
3. Evaluate the resulting simpler integral.
4. Convert from trigonometric functions back to the original variables.

Answer 1

• Use trigonometric substitution to evaluate integrals involving the square root of the sum or difference of two squares.

1. Match the square root expression with the sides of a right triangle.
2. Substitute the corresponding trigonometric function into the integrand.
3. Evaluate the resulting simpler integral.
4. Convert from trigonometric functions back to the original variables.