Q. 16

Using integration

Answer :

As first we need to trace the area to be determined.As x2+y2 = 4 represents a circle whose centre is at (0,0) and radius = 2 cm. The rough sketch is shown below:


As normal at (1,√3) passes through origin too because in a circle a normal always passes through centre of the circle.


Equation of normal is y = √3 x


Similarly equation of tangent can be written using one point and slope form.


As, x2 + y2 = 4


Differentiating w.r.t x:






We need to determine the area enclosed i.e. area(region ABC).


Area(region ABC) = area(region ABD) + area(region BDC)


Area = area under curve y = √3x + area under


Required area =


Area =


Area =


Area =


Required area =


OR


We know that a definite integral can be evaluated as a limit of a sum as-



Where h =


As we have to find:


Let I = and on comparing I with the formula we can say that a = 1 and b = 3.


I =


I = 2


I = 2


I = 2


Each bracket contains ‘n’ terms.


I = 2


I = 2


I = 2


Using formula for sum of first n natural numbers; sum of squares of first n natural numbers and sun of n terms of a GP we get:


I = 2


I = 2


As h =


I = 2


I = 2


Using algebra of limits:


I = 2


Use the formula:


I = 2


I =

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Evaluate:<span laMathematics - Board Papers

Evaluate:

Mathematics - Board Papers

Using integrationMathematics - Board Papers

Evaluate:

Mathematics - Board Papers

Evaluate:<span laMathematics - Board Papers

Evaluate:<span laMathematics - Board Papers