Question

Sol
***11. Find the area of the region enclosed by the curves y=4x- x?, y = 5-2x.(Mar-16 T.S)​

Answer 1

Answer:

3.75 units

Step-by-step explanation:

this can be done in two ways:

1. integration.

2. area of triangle(both equations are linear and forms triangle with x-axis)

ans:

method 2.

taking the two given equations and x-axis

y=4x-x=3x ----------------(1)

and y=5-2x --------------(2)

and y=0 ------------------(3)

the first point of the triangle is (0,0)

for second point:

solving (1) and (2) equations simultaneously

3x=5-2x

x=1

y=3x for x=1 gives y=3

therefore the second point is (1,3)

for the third point:

solving (2) and (3) simultaneously

5-2x=0

x=2.5

therefore third point is (2.5,0)

from the three point

p1=(10,0,) p2=(1,3) and p3=(2.5,0)

p1 and p2 forms the base and p3 forms the height of the triangle

therefore ans is 1/2*(2.5-0)*(3-0)=3.75

method 1. integration

integrating y=3x from x=0 to x=1

integration(3x.dx) from 0 to 1

= 3x^2/2 = 3/2 -----------(1)

then integrating y=5-2x from 1 to 2.5

= 5x-x^2= (5*2.5- 2.5^2) - (5*1-1)

=6.25-4=2.25 ---------(2)

ans= 3/2+2.25=3.75

formula used for integration is

f(x)=x^n

then integration(f(x))=x^(n+1)/n+1.