# What is the arclength of #f(x)=x^5-x^4+x # in the interval #[0,1]#?

##### 1 Answer

May 12, 2016

approximately

#### Explanation:

The arc length of the function

#s=int_a^bsqrt(1+(f'(x))^2)dx#

So, here, we see that since

#s=int_0^1sqrt(1+(5x^4-4x^3+1)^2)dx#

This can't be integrated by hand, so stick it into a calculator to see that

#sapprox1.42326#