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Single Variable Calculus

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Difficult

Integral with a Basic Trigonometric Substitution

SVCALC-WYEHDV

Evaluate the integral:

$$\int \sqrt{1-4x^2}dx$$

A

$\dfrac23(1-4x^2)^{\frac32} +C$

B

$\dfrac{\sin^{-1}(2x)}{4} +C$

C

$\dfrac{ \sin^{-1}(2x)}{4} +2\sqrt{1-4x^2}+C$

D

$\dfrac{ \sin^{-1}(2x)}{4} + \dfrac{x\sqrt{1-4x^2}}{2}+C$