Question

Find the area between the lines y = 3x. *
axis and the coordinates from x = 1 to x = 5.
12 sq unit
36 sq unit
O 28 sq unit
O 18 sq unit
nu​

Answer 1

Answer:

The line on the x-axis would have the equation y = 0, and we need to find the area between y = 3x and y = 0, from x = 1 to x = 5.

Method 1: Integration

Area

= Integral from x = 1 to x =5 (3x - 0)

= Integral from x = 1 to x = 5 (3x)

= function x = 1 to x = 5 (3x^2/2)

= (3*5^2/2) - (3 * 1^2/2)

= 75/2 - 3/2

= 72/2

= 36

Method #2: trapezoid area

The top base length is 3, the bottom base is 15, and the height is 4.

Area = (3 + 15) * (4)/2 = 18*2=36