Question

Assertion :Let $f\left(x\right)=min.\left(x+1,\sqrt{1-x}\right)$ , then area bounded by $y=f\left(X\right)$ & $x$-axis is $\frac{7}{6}$ square units. Reason: min of $f\left(x\right)=\{\begin{array}{cc}x+1& for-1\le x<0\\ \sqrt{1-x}& ,0<x\le 1\end{array}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Required area $=\left|{\int }_{-1}^0(x+1)dx\right|+\left|{\int }_0^1\sqrt{1-x}dx\right|=\frac{1}{2}+\frac{2}{3}=\frac{7}{6}$ square units.