Using integration find the area of the region bounded between the two circlesx^{2}+y^{2}=9 and (x-3)^{2}+y^{2}=9

 

 

Answers (1)

\\ \text { Point of intersection } \\ x^{2}+y^{2}=9....(i) \\ (x-3)^{2}+y^{2}=9 .....(ii)\\ $Equation (ii) -Equation (i) $ \\(x-3)^{2}-x^{2}=0 \\ (x-3-x)(x-3+x)=0 \\ x = \frac{3}{2}

x - cordinate of A = 3/2 

\\ \text { Required area = Area of OAB + Area of OCB = } 2 \times \text{Area of OAB } \\ = 2 [$ Area between OA and x -axis + Area between AB and x-axis $] \\ = 2 \left[\int_{0}^{\frac{3}{2}} \sqrt{9-(x-3)^{2}} d x+\int_{\frac{3}{2}}^{3} \sqrt{9-x^{2}} d x\right] \\ =4\left[\int_{\frac{3}{2}}^{3} \sqrt{9-x^{2}} d x\right] \\ =4\left[\frac{x}{2} \sqrt{9-x^{2}}+\frac{9}{2} \sin ^{-1} \frac{x}{3}\right]_{\frac{3}{2}}^{3} \\=4 \left(0+\frac{9\pi}{4} - \frac{9 \sqrt{3}}{8}-\frac{3\pi}{4} \right) \\= \left(6 \pi-\frac{9 \sqrt{3}}{2}\right)

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET Aug 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Knockout NEET Aug 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions