Question

How do you solve the integral ∫ᵈˣ/√(ₐ²₋ₓ²)?

a) Set x = asinθ
b) Set x = acosθ
c) Use the double angle formula
d) Apply the pythagorean identities

Answer 1

To solve the integral ∫ᵈˣ/√(ₐ²₋ₓ²), you can use the trigonometric substitution method. Start by setting x = asinθ and differentiate both sides to find dx = acosθ dθ. Next, substitute these values into the integral and simplify the expression.

Step-by-step explanation:

To solve the integral ∫ᵈˣ/√(ₐ²₋ₓ²), you can use the trigonometric substitution method. Start by setting x = asinθ.

Then, differentiate both sides to find dx = acosθ dθ. Next, substitute these values into the integral: ∫(acosθ)(a² - a²sin²θ)^(-1/2) dθ.

Simplify the expression and integrate using the appropriate techniques, such as a u-substitution.