To determine

To find:

The area of the region.

Solution:

15

Explanation

1) Concept:

The fundamental theorem of calculus part 2: If  f  is continuous on a,b, then ∫abfxdx=Fb-Fa,  where  F  is any antiderivative of f , that is, a function  F  such that F'=f .

2) Formula:

∫fx+gxdx=∫fxdx+∫gxdx

∫xndx=xn+1n+1+C

3) Given:

 y=x4 ;from y=0 to y=1

4) Calculation:

The curve x=y4 bounded between y=0 and y=1, is continuous on 0,1 then, thearea of the region enclosed by the given curve is

∫01y4dy

Solve this integral by using power rule of integration. Thus

∫01y4dy=y5501

Now by using the fundamental theorem of calculus,

y5501=155-0

By simplifying,

∫01y4dy=15

Conclusion:

Therefore, the area of the given region is 15.