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.You need to login to perform this action.
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