Calculus

Calculus of Parametric Equations

Parametric Equations - Area

         

What is the area between the xx-axis and the parametric curve x=6cos⁡θ,y=7sin⁡θx=6\cos \theta, y=7\sin \theta in the interval 0≤θ≤π?0 \leq \theta \leq \pi?

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What is the area of the region bounded by the xx-axis and the parametric curve x=t2y=3+18t−5t2\begin{array}{c}& x=t^2 & y=3+18t-5t^2 \end{array} in the interval 0≤t≤4? 0 \le t \le 4?

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What is the area between the xx-axis and the parametric curve defined by x=t,y=−t2+11?x=t, y=-t^2+11?

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What is the area between the xx-axis and the parametric curve defined by x=5t3x=5t^3 and y=ety=e^t in the interval 0≤t≤3?0 \leq t \leq 3?

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Let a,b,ka, b, k be positive integers such that 0<a<b<k 0 < a < b < k . Consider the points P=(−a,ka)P=(-a, ka) and Q=(b,kb)Q=(b, kb) which lie on the graph of y=k∣x∣y=k\lvert x \rvert . If the area of the region bounded by y=k∣x∣y=k\lvert x \rvert and the line segment PQPQ is 9595, what is kk?

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