#### 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.