Evaluate the definite integral. \int_{0}^{1}\frac{7}{1+x^{2}}dx

ArcactCatmedeq8 2021-11-19 Answered
Evaluate the definite integral.
0171+x2dx
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Expert Answer

Parminquale
Answered 2021-11-20 Author has 17 answers
Step 1
Refer to the question, we have to solve the definite integral a=0 and b=1 71+x2dx.
0111+x2
Step 2
Use the formula of integration of arctanx (x) to solve the provided integral
11+x2dx=tan1(x)
Then
0171+x2dx=7[tan1(x)]01
=7×π4
=7π4
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Oung1985
Answered 2021-11-21 Author has 16 answers
Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:
abf(x)dx=F(x)ab=F(b)F(a)
Step 2: In this case, f(x)=71+x2. Find its integral.
7tan1(x)01
Step 3: SInce F(x)ab=F(b)F(a), expand the above into F(1)−F(0):
7tan1(1)7tan1(0)
Step 4: Simplify.
7π4
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