Area Bounded by Curves
1-Find The Whole Area of The Curve
Last Updated: September 25, 2024Find The Whole Area of The Curve \(\pmb{ \left(y-x\right)^{2}-a^{2}+x^{2}=0}\) Answer: Here the given curve \begin{align} \pmb{ \left(y-x\right)^{2}-a^{2}+x^{2}=0} \end{align} Demonstration (a) To find the whole area : Let us first sketch the curve Putting \(\pmb{y=0 }\) in (1), we get \begin{align} &\pmb{ x^{2}-a^{2}+x^{2}=0}\nonumber\\ \implies & \pmb{ 2x^{2}=a^{2}}\nonumber\\ \implies & \pmb{ x=\pm \frac{a}{\sqrt{2}}}\nonumber\\ \end{align} ...
2-Find The Whole Area of The Curve
Last Updated: January 13, 2025Find The Whole Area of The Curve Show that the area of bounded by the hyperbola \(\pmb{x^{2}-y^{2}=c^{2} }\), X-axis and a line drawn from the origin to any point \(\pmb{(a,b) }\) of the curve is \(\pmb{\frac{c^{2}}{2} \log \left(\frac{a+b}{c} \right)}\) Answer: Here the given hyperbola is \begin{align} \pmb{x^{2}-y^{2}=c^{2} } \end{align} Also given that the point \(\pmb{(a,b)...
