Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDefinite Integration2 Marks
MCQ
$\int_{-2}^2\left|1-x^2\right| d x=$
A
2
✓
4
C
6
D
8
✓
Answer
Correct option: B.
4
(B) $\int_{-2}^2\left|1-x^2\right| d x$ $\begin{array}{l}=\int_{-2}^{-1}\left|1-x^2\right| d x+\int_{-1}^1\left|1-x^2\right| d x+\int_1^2\left|1-x^2\right| d x \\ =-\int_{-2}^{-1}\left(1-x^2\right) d x+\int_{-1}^1\left(1-x^2\right) d x-\int_1^2\left(1-x^2\right) d x \\ =-\left[x-\frac{x^3}{3}\right]_{-2}^{-1}+\left[x-\frac{x^3}{3}\right]_{-1}^1-\left[x-\frac{x^3}{3}\right]_1^2 \\ =\frac{4}{3}+\frac{4}{3}+\frac{4}{3}=4\end{array}$
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