Question

Find the area of the region bounded by the curve y=x3 and y=x+6 and x=0.

Answer 1

Step-by-step explanation:

let the three eqns 123

then find the value of x and put the value in y

Answer 2

Step-by-step explanation:

he required area is bounded between the points (0,0),(0,6),(2,8) which is shaded portion.

The required area A=∫20(y2−y1)dx.

Where y1=x3 and y2=x+6.

A=∫20(x+6)dx−∫20x3dx.

Step 2:

On integrating we get,

A=[x22+6x]20−[x44]20

On applying limits we get,

A=[222−0+6×2−0]−[244−0]

=[14−4]=10

Hence the required area=10 sq. units.