Find f.f'(t)=\frac{20}{1+t^2},\ f(1)=0

Carolyn Moore

Carolyn Moore

Answered question

2021-11-16

Find f.
f(t)=201+t2, f(1)=0

Answer & Explanation

Elizabeth Witte

Elizabeth Witte

Beginner2021-11-17Added 24 answers

Given, function is
f(t)=201+t2, f(1)=0
Integrate with respect to 't'
f(t)=f(t)+C
=201+t2+C
Apply the identity,
1a2+t2=1atan1(xa)
Hence,
f(t)=20tan1(t)+C
Apply initial condition,
f(1)=20tan1(1)+C
0=20tan1(tanπ4)+C
0=20π4+C
C=5π

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