Gi utregningen din da
Jada, jada. Mannen med fisken.
[tex] r(t) = [2 + t, - 0.5{t^2} + 3] [/tex]
[tex] r^{\prime}(t) = [1, - t] [/tex]
[tex] \left| {r^{\prime}(t)} \right| = \sqrt {{t^2} + 1}[/tex]
[tex] f\left( x \right) = \int {\sqrt {{t^2} + 1} } [/tex]
Bruk substitusjonen [tex] x = \sinh(t) \, dt = \cosh(t) dt[/tex]
[tex] f\left( x \right) = \frac{1}{2}x\sqrt {{x^2} + 1} + \frac{1}{2}\arcsin \text{h} \left( x \right) [/tex]
[tex]\tex{Nedre grense}[/tex]
[tex] f\left( { - 2} \right) = - \sqrt 5 - \frac{1}{2}\arcsin \text{h} \left( 2 \right) [/tex]
[tex]\tex{Ovre grense}[/tex]
[tex] f\left( 2 \right) = \sqrt 5 - \frac{1}{2}\arcsin \text{h} \left( 2 \right) [/tex]
[tex] f\left( { - 2} \right) + f\left( 2 \right) = 2\sqrt 5 + \arcsin \text{h} \left( 2 \right) [/tex]
[tex] \underline{\underline {{\rm{ }}2\sqrt 5 + \arcsin \text{h} \left( 2 \right){\rm{ }}}} [/tex]
Mellomregningene får du ta deg av^^
EDIT ops
[tex]\arcsin \text{h} ( x ) = ln( x + sqrt{1 + x^2}) [/tex]