Vault Of Euclid

Integral Yielding an Arcsine Function

Trigonometric and inverse trigonometric functions warmup

\[ \int \frac{dx}{\sqrt{25-x^2}} \]

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Integration by substitution
Derivatives of inverse trigonometric functions
Algebraic simplification of square roots

What this problem tests

Tests the ability to recognize the form of an inverse trigonometric integral and apply the correct substitution to evaluate it.

This is a standard introductory problem in Calculus I when learning about integrals that result in inverse trigonometric functions.

More on Trigonometric and inverse trigonometric functions

Tangent Line to Sine Squared warmup
Derivative of Cosine Squared warmup
Horizontal Tangents of the Secant Function warmup
Derivative of 2 tan(x/2) - 5 warmup
Derivative of x^2 cos(2x) warmup
Integral Yielding an Inverse Tangent warmup

← today's set