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If the ordinate x=a divides the area bounded by the curve Y = 1 + 8/x 2 and the ordinates x=2, x=4 into two equal parts, then a is equals to (a) 2 √3 (b) 2√2 (c) 3 (d) none of these
Area under the curve from x=2 to 4 will be 4. This is obtained by simple integration of the given function which is x - 8/x. Let A be a point between x=2 and 4. So the integral reduces to int(1+8/x^2) from x=2 to A + int(1+8/x^2) from x=A to 4. But as said the point divides the area into two equal parts. So int(1+8/x^2) from x=2 to A is equal to int(1+8/x^2) from x=A to 4. So 4=2 int(1+8/x^2) from x=2 to A. Solving this, we get the value for A to be option B
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