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The area of the region bounded by the curve y = f(x), x axis and the lines x = a and y = b, (b > a) is given by1. \(\displaystyle\int_a^b x \ dx\)2. \(\displaystyle\int_a^b y \ dy\)3. \(\displaystyle\int_a^b y \ dx\)4. \(\displaystyle\int_a^b x \ dy\) |
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Answer» Correct Answer - Option 3 : \(\displaystyle\int_a^b y \ dx\) Explanation: Area enclosed by a curve y = f (x) and x axis is given by: A = ∫ f (x) dx Since curve is bounded by lines x = a and y = b i.e Lower limit for x = a and upper limit for x = b (∵ b > a) ∴ \(A=\displaystyle\int_a^b f(x) \ dx\) Since f(x) = y Hence \(A=\displaystyle\int_a^b y \ dx\) |
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