The area of the region enclosed by the curves: Y = 3X and Y = 6X² is
1/8 sq. unit.
Linear equation are those in which power is 1 or maximum degree is 1. For example: x + y = 3 here the maximum degree is 1.
Quadratics equation are those in which power is 2 or maximum degree is 2. For example: X² + 6X + 3 = 0. here the maximum degree is 2.
Here, we have given two equation:
Y = 3X
Y = 6X²
To find the limit we will equate the both equation:
3X = 6X²
6X² - 3X = 0
3X ( 2X - 1 ) = 0
here we get two values of X, X = 0 and X = 1/2
so, Lower limit = 0 and Upper limit = 1/2.
Area = [tex]\int\limits^ \frac{1}{2} _0 {(3x - 6x^{2} ) } \, dx[/tex]
Area = ( 3/2 ( x ⁸ ) - 2 ( x³ ) ) --- Limit from: 0 to 1/2
Area = (3/2 ( 1/2 ² ) - 2 ( 1/2 ³) ) - ( 3/2 ( 0² ) - 2 ( 0³) )
Area = 3/8 - 1/4 - 0 + 0
Area = 1/8 sq. unit
Hence,
The area of the region enclosed by the curves: Y = 3X and Y = 6X² is
1/8 sq. unit. For graph See the attached image.
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