Let f(x)=sinx. Calculate the arc length of the graph of f(x) over the interval [0,π]
We will need √(1 + cos^2 x) dx from 0 to π
there is no actual integral of this, so numerical methods have to be used,
which are clearly beyond the scope of this website, and especially the
capability of this poor bot.
The above answer is just silly
The arc length of the graph of f(x) over the interval [0,π] is 2.
The formula for arc length is:
Arc Length = ∫a b √1+(f'(x))2dx
In this case, f'(x) = cosx
Therefore, the arc length of the graph of f(x) over the interval [0,π] is:
Arc Length = ∫0 π √1+(cosx)2dx
Arc Length = ∫0 π √1+cos2x dx
Arc Length = ∫0 π √2 dx
Arc Length = ∫0 π √2 dx
Arc Length = 2√2
Arc Length = 2