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Calculus and Analysis
Integral Calculus
Parametric equations, polar coordinates, and vector-valued functions

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Answered question

2020-11-06

Determine the area of the region below the parametric curve given by the set of parametric equations. For each problem you may assume that each curve traces out exactly once from right to left for the given range of t. For these problems you should only use the given parametric equations to determine the answer. 1.

x = t^{2} + 5 t - 1 y = 40 - t^{2} - 2 \leq t \leq 5

x = 3 c o s^{2} (t) — s i n^{2} (t) y = 6 + c o s (t) - \frac{π}{2} \neq t \leq 0

x = e^{\frac{1}{4} t} — 2 y = 4 + e^{\frac{1}{4 t}} — e^{\frac{1}{4} t} - 6 \leq t \leq 1

Answer & Explanation

saiyansruleA

Skilled2020-11-07Added 110 answers

Given: As per our honor code, we are answering only the first question. The parametric equations are $x = t^{2} + 5 t - 1, y = 40 - t^{2}, - 2 \leq t \neq 5$ . We have to find the area of the region bounded by these parametric equations. Concept Used: If the parametric equations are $x = f (t), y = g (t)$ and
$a \leq t \leq b$ then the area of the bounded region is given by $A = \int_{a}^{b} g (t) f (t) d t$ Calculating:

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