Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Calculus

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 - Surface Area

What is the surface area $S$ of the body of revolution obtained by rotating the curve $y=e^x,$ $0 \le x \le 1,$ about the $x-$ axis?

\displaystyle{ \pi \left( e\sqrt{4+e^2}+\ln(e+\sqrt{4+e^2})-\sqrt{2}- \ln(\sqrt{2}+4)\right)}

\displaystyle{ \pi \left( e\sqrt{2+e^2}+\ln(e+\sqrt{2+e^2})-\sqrt{2}- \ln(\sqrt{2}+2)\right)}

\displaystyle{ \pi \left( e\sqrt{3+e^2}+\ln(e+\sqrt{3+e^2})-\sqrt{2}- \ln(\sqrt{2}+3)\right)}

\displaystyle{ \pi \left( e\sqrt{1+e^2}+\ln(e+\sqrt{1+e^2})-\sqrt{2}- \ln(\sqrt{2}+1)\right)}

Show explanation

View wiki

by Brilliant Staff

What is the surface area $S$ of the body of revolution obtained by rotating the parametric curve $\begin{array}{c}&x = 8 t^2 + 9 &y = -4 t &0 \leq t \leq 1 \end{array}$ about the $x$ -axis?

\displaystyle{ \left(\frac{2}{3} - \frac{17\sqrt{272} }{6}\right)\pi}

\displaystyle{ \left(\frac{256}{385} - \frac{544\sqrt{272} }{197}\right)\pi}

\displaystyle{ \left(\frac{256}{387} - \frac{1088\sqrt{272} }{389}\right)\pi}

\displaystyle{ \left(\frac{32}{49} - \frac{272\sqrt{272} }{97}\right)\pi}

Show explanation

View wiki

by Brilliant Staff

What is the surface area $S$ of the solid of revolution obtained by rotating the parametric curve $\begin{array}{c}&x = 4 t &y = 6 t &0 \leq t \leq 2 \end{array}$ about the $y$ -axis?

8 \sqrt{52} \pi

8 \sqrt{20} \pi

16 \sqrt{52} \pi

16 \sqrt{20} \pi

Show explanation

View wiki

by Brilliant Staff

What is the surface area $S$ of the body of revolution obtained by rotating the parametric curve $\begin{array}{c}&x = 7 \cos t &y = 7 \sin t &0 \leq t \leq \pi \end{array}$ about the $x$ -axis?

196 \pi

98 \pi

49 \pi

Show explanation

View wiki

by Brilliant Staff

If $S$ is the surface area of the solid obtained by rotating the parametric curve $\begin{array}{c}&x = 4 \cos^3 t &y = 4 \sin^3 t &0 \leq t \leq \frac{\pi}{2} \end{array}$ about the $x$ -axis, what is $\frac{5}{2}S?$

43 \pi

48 \pi

51 \pi

45 \pi

Show explanation

View wiki

by Brilliant Staff