Question

Find the area of the region bounded by y=2x y=0 x=0 and x=2

Answer 1

between x=0 and x=2 graph of y=2x is above x axis which means area is positive. so you can direct integrate the function y=2x to get you answer as

y= 2§x with the limit 0 to 2.
=2x²/2-0
=2*4/2
=8/2
=4 sq. unit

i hope this will help you

Answer 2

Answer:

The area of the region = 4 sq. units

Step-by-step explanation:

y=2x is a linear line graph,

given the limits x=0 to x=2, it lies on the positive x axis.

To find the area of an equation, we need to find the first integral of the equation within the limits 0 $- >$ 2.

(Formula to find integral ⇒ $\int{ x^{n}} \, dx = \frac{x^{n+1} }{n+1}$   )

On integrating y=2x with respect to 'x',

                             ∴  $\int\limits^2_0 {2x} \, dx = 2\int\limits^2_0 {x} \, dx$

                                              $= 2 { \frac{x^{1+1}}{2} ^{2}_{0} }$

                                               $= 2 { \frac{x^{2}}{2} ^{2}_{0} }$

• Given, Let the upper limit be denoted by b = 2

                  and the lower limit is denoted by a = 0.

                                                $= 2 { \frac{b^{2}-a^{2}}{2}}$

2 divided by 2 is 1.

                            ∴    $\int\limits^2_0 {2x} \, dx = 2^{2}-0x^{2}$

                                  $\int\limits^2_0 {2x} \, dx = 4 sq.units$  

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