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10 cards from this deck
Use x=atanθx = a \tan \thetax=atanθ for ellipse shape.
Use x=asecθx = a \sec \thetax=asecθ, sometimes atanθa \tan \thetaatanθ.
Integral becomes ∫4cos2θdθ\int 4 \cos^2 \theta d\theta∫4cos2θdθ.
Use 1+tan2θ=sec2θ1 + \tan^2 \theta = \sec^2 \theta1+tan2θ=sec2θ.
Substitute x=asinθx=a \sin \thetax=asinθ, then integrate.
To match xxx-limits to θ\thetaθ-values.
Use x=asecθx=a\sec\thetax=asecθ, or sometimes atanθa \tan \thetaatanθ.
Use x=asinθx=a\sin \thetax=asinθ, transform integrand.
x=asinθx=a\sin\thetax=asinθ, x=atanθx=a\tan\thetax=atanθ, x=asecθx=a\sec\thetax=asecθ.
Use x=3sinθx=3 \sin \thetax=3sinθ, then integrate.
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