KVPY 2019 SB SX Exam Previous Papers

© examsiri.com

Question : 3 of 120

Marks: +1, -0

The area of the region bounded by the lines x = 1, x = 2, and the curves

x(y -e^x) = \sin x

and

2xy = 2\sin x +x^3

is

$e^2 -e -1/6$
$e^2 -e -7/6$
$e^2 -e +1/6$
$e^2 -e +7/6$

Solution:

y =e^ x+{ \sin x}/x

and

y = {\sin x}/x + x^ 2/2

Area =

∫↖{2}↙{1}[(e^x+{ \sin x}/x )-(x^2/2+{ \sin x}/x )]dx

={|e^x-x^3/6|}^2_1

=e^2-4/3-e+1/6

=e^2-e-7/6

© examsiri.com

Go to Question:

Prev Question

Next Question