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NCERT Class XII Mathematics Chapter - - Solutions

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Exercise - 7.7
Integrate the functions in Exercises 158 to 166.
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Question : 159 of 271
Marks: +1, -0
1−4x2\sqrt{1-4x^2}
Solution:  
∫1−4x2 dx\int\sqrt{1-4x^2}\,dx =2∫(12)2−x2 dx=2\int\sqrt{\left(\frac{1}{2}\right)^2-x^2}\,dx
=2[x2(12)2−x2+18sin⁡−1(x12)]+C=2\left[\frac{x}{2}\sqrt{\left(\frac{1}{2}\right)^2-x^2}+\frac{1}{8}\sin^{-1}\left(\frac{x}{\frac{1}{2}}\right)\right]+C
=x1−4x22+14sin⁡−1(2x)+C=\frac{x\sqrt{1-4x^2}}{2}+\frac{1}{4}\sin^{-1}(2x)+C
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