Question

Find the area of the region bounded by the curve y = 2x & the lines X=0 & y=1.​

Answer 1

Answer:

Required area = Area of ABCD = ∫

1

4

ydx

=∫

1

4

x

dx

=

3

2

[(4)

3/2

−(1)

3/2

]

=

3

2

(8−1)=

3

14

units

Answer 2

Step-by-step explanation: The given curve is y = 2x, and it intersects the y-axis at the origin (0, 0) and the line y = 1 when x = 1/2.

To find the area of the region bounded by the curve and the lines x = 0 and y = 1, we need to integrate the function y = 2x with respect to x, from x = 0 to x = 1/2.

So the area is given by:

Area = ∫[0, 1/2] 2x dx

= [x^2]0^1/2

= (1/2)^2 - 0^2

= 1/4

Therefore, the area of the region bounded by the curve y=2x and the lines x=0 and y=1 is 1/4 square units.

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