Practicing Success
Practicing Success
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Area bounded by $|x-1|≤2$ and $x^2-y^2 =1$, is |
$6\sqrt{2}+\frac{1}{2}ln|3+2\sqrt{2}|$ $6\sqrt{2}+\frac{1}{2}ln|3-2\sqrt{2}|$ $6\sqrt{2}-\frac{1}{2}ln|3+2\sqrt{2}|$ none of these |
none of these |
We have, $|x-1|≤2⇔-1≤x≤3$ ∴ Required area A is the area of the shaded region and is given by $A=2\int\limits_{1}^{3}\sqrt{x^2-1}dx$
$⇒A=\left[x\sqrt{x^2-1}-\log_e(x+\sqrt{x^2-1})\right]_1^3$ $⇒A=\left\{3\sqrt{8}-\log_e(3+\sqrt{8})\right\}=6\sqrt{2}-\log_e(3+2\sqrt{2})$ |
