Calculus of Parametric Equations

Concept Quizzes

Parametric Equations - Derivative
Parametric Equations - Tangent
Parametric Equations - Area
Parametric Equations - Arc Length
Parametric Equations - Velocity and Acceleration
Parametric Equations - Surface Area
Parametric Equations - Volume

Challenge Quizzes

Parametric Equations Calculus: Level 3 Challenges

Parametric Equations - Area

What is the area between the $x$ -axis and the parametric curve $x=6\cos \theta, y=7\sin \theta$ in the interval $0 \leq \theta \leq \pi?$

21\pi

42\pi

63\pi

84\pi

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

304\sqrt{2}

176 304

176\sqrt{2}

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

\displaystyle{ \frac{22\sqrt[3]{11}}{3}}

\displaystyle{ \frac{22\sqrt{11}}{3}}

\displaystyle{ \frac{44\sqrt[3]{11}}{3}}

\displaystyle{ \frac{44\sqrt{11}}{3}}

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

75e^{3}-30\

75e^{3}\

75e^{3}+15\

75e^{3}-15\

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Let $a, b, k$ be positive integers such that $0 < a < b < k$ . Consider the points $P=(-a, ka)$ and $Q=(b, kb)$ which lie on the graph of $y=k\lvert x \rvert$ . If the area of the region bounded by $y=k\lvert x \rvert$ and the line segment $PQ$ is $95$ , what is $k$ ?

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