Practice: Area Under the Parametric Curve

Calculus w/ Parametric Curves

9 Activities

Practice Question
Write down the integral representing the area under the curve parameterized by x=2tan⁡tx = 2\tan tx=2tant, y=2ty = 2ty=2t, for 0≤t≤π/40 \le t \le \pi/40≤t≤π/4. 
  

2∫0π/4 sec⁡2t  ⁣dt2{\displaystyle\int}^{\pi/4}_0\ \sec^2 t\de{t}2∫0π/4​ sec2t dt

∫0π/4t2 sec⁡2t  ⁣dt{\displaystyle\int}^{\pi/4}_0t^2\ \sec^2 t\de{t}∫0π/4​t2 sec2t dt

∫0π/4t sec⁡2t  ⁣dt{\displaystyle\int}^{\pi/4}_0t\ \sec^2 t\de{t}∫0π/4​t sec2t dt

4∫0π/4t sec⁡2t  ⁣dt4{\displaystyle\int}^{\pi/4}_0t\ \sec^2 t\de{t}4∫0π/4​t sec2t dt

4∫0π/4t2 sec⁡2t  ⁣dt4{\displaystyle\int}^{\pi/4}_0t^2\ \sec^2 t\de{t}4∫0π/4​t2 sec2t dt

I don't know

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Practice: Area Under the Parametric Curve

Find the area under the curve {x=t2, y=cos⁡t: t∈[0,π2]}\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}{x=t2, y=cost: t∈[0,2π​]}.

Practice: Area Under the Parametric Curve

Practice Question
Find the area under the cruve {x=t2, y=cos⁡t: t∈[0,π2]}\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}{x=t2, y=cost: t∈[0,2π​]}.

Practice: Area Under the Parametric Curve

Practice Question
Find the area under the cruve {x=t2, y=cos⁡t: t∈[0,π2]}\left\{x=t^2,\ y=\cos t:\ t\in\left[0,\frac{\pi}{2}\right]\right\}{x=t2, y=cost: t∈[0,2π​]}.

⭐ TRICKY! Find, if possible, the maximum and minimum values of the curvature of the graph of y = ex  and the points at which they occur. 

Practice: Area Under the Parametric Curve

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Calculus w/ Parametric Curves

Practice Question

More Calculus w/ Parametric Curves Questions:

Practice: Area Under the Parametric Curve

Practice: Area Under the Parametric Curve

Practice: Area Under the Parametric Curve