Math Problem Statement

Evaluate the definite integrall from 0 to 1/4. it is 2/sqrt(1-4x^2). dx

Solution

To evaluate the integral

∫01/421−4x2 dx,\int_{0}^{1/4} \frac{2}{\sqrt{1 - 4x^2}} \, dx,

Step 1: Recognize the form of the integral

The integrand is of the form 11−u2\frac{1}{\sqrt{1 - u^2}}, which resembles the derivative of arcsin⁡(u)\arcsin(u).

Here, let: [ u = 2x, \quad \text{so

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Math Problem Analysis

Mathematical Concepts

Calculus
Definite Integration
Trigonometric Substitution

Formulas

Integral of 1/sqrt(1-u^2) is arcsin(u) + C

Theorems

Fundamental Theorem of Calculus

Suitable Grade Level

Grades 11-12

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