Question

Find the area bounded by the lines x=0,y=1,y=x using double integration

Ops:

A. 1 square units

B.2 square units

c. 4 square units

D. 1/2 square units​

Answer 1

Answer:

a option is correct

Step-by-step explanation:

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Answer 2

Answer:

option d. the area bounded by the lines is $\frac{1}{2} sq units$

Step-by-step explanation:

In the graph

Red line - y=x

Blue line - x=0

Green line - y=1

The graph shows the lines x=0, y=x, y=1 and their intersection point just to give idea about the shape.

When x=0 then y=0

$x=0\\y=x\\y=0\\\\y=1\\y=x\\x=1$

When y = 1 then x=1

The coordinates of the area enclosed is (0,0) , (1,0), (0,1).

In double integration, the first integration of x coordinate with respect to y and then integrate y coordinate with respect to limits. Double integration takes the entire 2-dimensional area so it is good to find area of a two-dimensional shape.

$\int\limits^1_0 {\int\limits^y_0 \, dx } \, dy \\=\int\limits^1_0 {y} \, dy\\ =\frac{1}{2}sq units$