Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integrals2 Marks
Question
Write a value of $\int\sqrt{4-\text{x}^2}\text{ dx}$
✓
Answer
Let $\text{I}=\int\sqrt{4-\text{x}^2}\text{ dx}$
We know that,
$\int\sqrt{\text{a}^2-\text{x}^2}=\frac{\text{x}}{2}\sqrt{\text{a}^2-\text{x}^2}+\frac{\text{a}^2}{2}\sin^{-1}\frac{\text{x}}{\text{a}}+\text{C}$
Thus here a = 2
$\therefore\ \text{I}=\frac{\text{x}}{2}\sqrt{4-\text{x}^2}+2\sin^{-1}\frac{\text{x}}{2}+\text{C}$
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