Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent

geduiwelh 2021-09-11 Answered

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not, state your answer as "divergent".
3(8(x+4)3/2)

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Expert Answer

Luvottoq
Answered 2021-09-12 Author has 95 answers

Compute the definite integral:
34(x+4)3dx
Factor out constants:
=431(x+4)3dx
For the integrand 1(x+4)3, substitute u = x + 4 and du = dx.
This gives a new lower bound u=4+3=7 and upper bound u=:
=471u3du
Apply the fundamental theorem of calculus.
The antiderivative of 1u3is12u2:
=limb(2u2)|7b
Evaluate the antiderivative at the limits and subtract.
(2u2)|7=(22)(272)=249:
Answer:
=249

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