Question

Hello, how do you findd the area of the indicated region between y=x^3 and y= -1 for x in [-1, 1]

Answer 1

see the attached figure to better understand the problem

step 1

Find out the area of the function y=-1 , in the interval [-1,0]

A=(1)*(1)=1 unit2

Find out the area of the function y=x^3 in the interval [-1,0]

`\int ^0_(-1)x^3dx=-(1)/(4)`

the area of the shaded region in the interval [-1,0] is

A=1-(1/4)=3/4 unit2

step 2

Find out the area of the function y=-1 in the interval [0,1]

A=(1)*(1)=1 unit2

Find out the area of the function y=x^3 in the interval [0,1]

`\int ^1_0x^3dx=(1)/(4)`

the area of the shaded region in the interval [0,1] is

A=1+1/4=5/4 unit2

the total area is

(3/4)+(5/4)=8/4=2 unit2