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If f(x) is an even function and a is a positive real number, then $$\int_{ - {\text{a}}}^{\text{a}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$   equals

If f(x) is an even function and a is a positive real number, then $$\int_{ - {\text{a}}}^{\text{a}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$   equals Correct Answer $$2\int_0^{\text{a}} {{\text{f}}\left( {\text{x}} \right){\text{dx}}} $$

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There are two rows, each containing 3 numbers. Below are some rules to be used to get the resultant number for each row separately. Use the rule from left to right for each row and find the answer to the question. Rule: 1. If an even number is followed by an even number, then the first number will be subtracted from the second. 2. If an odd number is followed by an odd number, then both will be added. 3. If an odd number is followed by an even number, then the even number will be subtracted from the square of the odd number. 4. If an even number is followed by an odd number, then the odd number will be subtracted from the even number. Row I: 9,11, 34 Row II: 16, 9, 8 What is the difference between the resultant numbers in the first row and the second row
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Complex Variable mcq question image
The value of $$I$$ is
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$${\text{f}}\left( {\text{x}} \right) = \frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}$$     where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral $$\int_{ - \infty }^{\text{a}} {\frac{1}{{\sqrt {2\pi } * {\text{b}}}}{{\text{e}}^{\frac{{ - 1}}{2}{{\left( {\frac{{{\text{x}} - {\text{a}}}}{{\text{b}}}} \right)}^2}}}{\text{dx}}} $$
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