Question

d) The trifolium of Descartes: $\begin{cases} x(t) = r(t) \cos(t) \\ y(\varphi) = r(t) \sin(t) \end{cases}$ avec $r(t) = \cos(3t)$ avec $t \in [0; \pi]$. 1/ Calculate the length of Trifolium using $\int_a^b \sqrt{x'(t)^2 + y'(t)^2}dt$ 2/ Calculate the exact value of the area of the surface bounded by Using this area formula $= \frac{1}{2} \left| \int_a^b (x(t)y'(t) - x'(t)y(t))dt \right|$

          d) The trifolium of Descartes:
$\begin{cases} x(t) = r(t) \cos(t) \\ y(\varphi) = r(t) \sin(t) \end{cases}$
avec $r(t) = \cos(3t)$ avec $t \in [0; \pi]$.
1/ Calculate the length of Trifolium using $\int_a^b \sqrt{x'(t)^2 + y'(t)^2}dt$
2/ Calculate the exact value of the area of the surface bounded by
Using this area formula $= \frac{1}{2} \left| \int_a^b (x(t)y'(t) - x'(t)y(t))dt \right|$

d) The trifolium of Descartes:
x(t) = r(t) cos(t)
y(φ) = r(t) sin(t)
avec r(t) = cos(3t) avec t ∈ [0; π].
1/ Calculate the length of Trifolium using ^b √(x'(t)^2 + y'(t)^2)dt
2/ Calculate the exact value of the area of the surface bounded by
Using this area formula = (1)/(2)| ^b (x(t)y'(t) - x'(t)y(t))dt |

Added by Christian K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Donna Densmore

11/04/2022

Step 1

x'(t) = r'(t)cos(t) - r(t)sin(t) y'(t) = r'(t)sin(t) + r(t)cos(t) Show more…

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Thanks for your feedback!

Sure, I'd be happy to help with your math questions. Here are the corrected texts: d) The triffolium of Descartes: x(t) = r(t)cos(t) y(t) = r(t)sin(t) avec r(t) = cos(3t) avec t in [0;π]. 1/ Calculate the length of Triffolium using ∫[a to b] √(x'(t)^(2) + y'(t)^(2))dt 2/ Calculate the exact value of the area of the surface bounded by Using this area formula = (1)/(2) * ∫[a to b] (x(t)y'(t) - x'(t)y(t))dt