Q. 235.0( 1 Vote )

Evaluate <span la

Answer :

Know that, limit of sums is the sum of limits of the function.

We have,


Let f(x) = 3x2+ 2x …(i)


Here,


a = 1


b = 3


nh = b – a = 3 – 1 = 2 …(*)


We know limit of sums is given as,



Put a = 1 as deduced above.



Put x = 1 in (i),


f(1) = 3(1)2 + 2(1)


Put x = 1 + h in (i),


f(1 + h) = 3(1 + h)2 + 2(1 + h)


Repeat the same for other values of x. We get,











From (*), nh = 2





=10+8+16



OR


We have two equations:





Let us take equation of ellipse and find y.






Taking square root on both sides,




Let it be y1, such that


…(i)


Let us take equation of straight line and find y.






Let it be y2, such that


…(ii)


Put in .



√(9 – x2) = 3 – x


Squaring on both sides, we get


[√(9 – x2)]2 = (3 – x)2


9 – x2 = 9 + x2 – 6x


x2 + x2 + 9 – 9 – 6x = 0


2x2 – 6x = 0


2x(x – 3) = 0


2x = 0 or (x – 3) = 0


x = 0 or x = 3


Put x = 0 in .




y = 2


Put x = 3 in .




y = 0


One point of intersection is (0, 2) and the other point of intersection is (3, 0).


So, the area of the region is given by



Putting the values of y1 and y2 from (i) and (ii) in the above equation, we get















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 :

Draw a rough sketMathematics - Exemplar

Compute the area Mathematics - Exemplar

Using integrationMathematics - Board Papers

Find the area of Mathematics - Board Papers

Find the area of Mathematics - Exemplar

Evaluate <span laMathematics - Board Papers

The area of the rMathematics - Exemplar

Find the area bouMathematics - Exemplar