For problems 1 the area of the region below the parameric curve given

Baublysiz

Baublysiz

Answered question

2021-11-30

For problems 1 the area of the region below the parameric 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=t2+5t1
y=40t2
2t5

Answer & Explanation

Jeffrey Parrish

Jeffrey Parrish

Beginner2021-12-01Added 15 answers

Step 1
Given,
As per our honor code, we are answering only the first question.
The parametric equations are x=t2+5t1, y=40t2, 2t5 We have to find the area of the region bounded by these parametric equations.
Step 2
If the parametric equations are x=f(t), y=g(t) and atb then the area of the bounded region is given by
A=abg(t)f(t)dt
Step 3
f(t)=x=t2=5t1f(t)=2t+5
g(t)=y=40t2
Hence the area is
A=abg(t)f(t)dt
=25(40t2)(2t+5)dt
=25(80t2t25t2+200)dt
=[80t222t445t33+200t]25
=[40t2t425t33+200t]25
=[100062526253+1000][1608+403400]
=200031256+248403
=2248+534.166
=2782.162

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