question_answer

Direction: Question No. 93 is Assertion-Reason type question. These question contains two statements: Statement I (Assertion) and Statement II (Reason). These question also has four alternative choices, only one of which is the correct answer. You have to select the correct choice in the cedes (a), (b), (c) and (d) in the given below:  

Statement I: \[\int_{-1}^{1}{|x|dx}\] can be found while \[\int_{{}}^{{}}{|x|dx}\] cannot be found.

Statement II: |x| is non-differentiable at x = 0.

A)  Statement I is true. Statement J fin true; Statement B is not a correct explanation for Statement I.

B)  Statement I is true. Statement II is false.

C)  Statement 1 is false. Statement S is true.

D)  Statement I is true, Statement H is true; Statement H is a correct explanation for Statement I.

Correct Answer: A

Solution :

Given, \[\int_{-1}^{1}{|x|dx=\int_{-1}^{a}{|x|dx+\int_{0}^{1}{|x|dx}}}\] \[=\int_{-1}^{0}{(-x)dx+\int_{0}^{1}{(x)dx}}\] \[=-\left[ \frac{{{x}^{2}}}{2} \right]_{1}^{0}+\left[ \frac{{{x}^{2}}}{2} \right]_{0}^{1}\] \[=-\left( 0-\frac{1}{2} \right)+\left( \frac{1}{2}-0 \right)=1\] and \[\int_{{}}^{{}}{|x|dx}\] cannot be found, since condition on x is not given. Also, |x| is non-differentiable at x = 0.