Question

PLEASE HELP 20 POINTS AND BRAINLIEST TO WHOEVER ANSWERS FIRST
sketch the region enclosed by the lines x=0 x=6 y=2 and y=6 find the area of the region

Answer 1

Answer:

24 units²

Step-by-step explanation:

Given:

• Region enclosed by the line x = 0, x = 6, y = 2 and y = 6.

To find:

• Sketch
• Area

The area enclosed by these lines can be expressed as:

$\displaystyle \large{\int_0^6 \int_2^6 dy dx }$

For:

$\displaystyle \large{\int_2^6 dy}$

Recall:

$\displaystyle \large{\int_a^b dy = [y]_b^a = a-b}$

Therefore:

$\displaystyle \large{\int_2^6 dy = [y]_2^6 = 6-2 = 4}$

Now we we have:

$\displaystyle \large{\int_0^6 4dx}$

Recall:

$\displaystyle \large{\int_a^bk dx = [kx]_a^b = kb-ka}$

for k = constant

Therefore:

$\displaystyle \large{\int_0^6 4 dx = [4x]_0^6 = 4(6)-4(0) = 24}$

Hence, the area of region is 24 units²