Question

area of the region between the curve y= 4x^2 and the line y= 6x-2 is​

Answer 1

Answer:y=4x-x^2………(1). and. y= 5–2x……………….(2). from eqn.(1). & (2)

5–2x=4x-x^2

or. x^2-6x+5=0

or. (x-1).(x-5)=0

or. x= 1 , 5. and y=5–2.1. , 5–2.5. or. 3 , -5

Point of intersection are (1 , 3) and (5 , -5)

Required area=integ.of (lim 1 to 5)[(4x-x^2).dx] - integ.of (lim 1 to 5)[(5–2x).dx]

=[2x^2-x^3/3](lim 1 to 5) -[5x-x^2](lim 1 to 5).

=[(50–125/3)-(2–1/3)]-[(25–25)-(5–1)]

=(25/3–5/3)-(0–4)

= 20/3+4

= 32/3 sq.units. Answer

Answer 2

Answer:

1/12 square units

hope it helps