JEE Mains · Maths · STD 12 - 8. Application and integration
If the area of the region bounded by the curves, \(y = {x^2}\,,\,y = \frac{1}{x}\) and the lines \(y = 0\) and \(x = t (t > 1 )\) is \(1\,sq. unit\) , then \(t\) is equal to
- A \(\frac {4}{3}\)
- B \(e^{2/3}\)
- C \(\frac {3}{2}\)
- D \(e^{3/2}\)
Answer & Solution
Correct Answer
(B) \(e^{2/3}\)
Step-by-step Solution
Detailed explanation
The intersection point of \(y=x^{2}\) and \(y=\frac{1}{x}\) is \((1,1)\) Area bounded by the curves is the region \(\mathrm{ABCDA}\) is given as: \({\rm{ Area }} = \int_0^1 {{x^2}} dx + \int_1^t {\frac{1}{x}} dx\)…
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