Calculus

Arc Length and Surface Area

Arc Length by Integration

         

If f(x)=x41, {f}'(x) = \sqrt{ {x}^4-1 }, what is the length of the curve y=f(x)y = f(x) from x=2x = 2 to x=8?x = 8?

What is the length of the curve y=12(ex+ex)y = \frac{1}{2}( {e}^x+{e}^{-x} ) from x=13x = -13 to x=13x = 13?

Let LL be the length of the line y=3x+4y = 3x + 4 on the interval 3x83 \leq x \leq 8. If L=aL = \sqrt{a}, then what is the value of aa?

Given y0,y \geq 0 , what is the length of the curve y2=x3{y}^2 = {x}^3 on the interval 0x40 \leq x \leq 4?

Let LL be the length of the curve y=14x212lnx\displaystyle{y = \frac{1}{4}{x}^2 - \frac{1}{2} \ln x } for 4x8.4 \leq x \leq 8. If L=a+12lnb,L = a+\frac{1}{2}\ln{b} , where aa and bb are positive integers, what is the value of a+b?a+b?

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