Evaluate the definite integral. \int_{0}^{4}\frac{5}{3x+1}dx

scottyqegi

scottyqegi

Answered question

2021-11-20

Evaluate the definite integral.
0453x+1dx

Answer & Explanation

George Blue

George Blue

Beginner2021-11-21Added 18 answers

Step 1
we have the integral
0453x+1dx
we will use the formula
1ax+bdx=1alog(ax+b)+c
Step 2
integrating it we get
[53log(3x+1)]04
=(53log(3(4)+1))(53log(3(0)+1))
=(53log(13))(53log(1))
=53log(131)
=53(1.11)
=1.85
Step 3
hence the value is 1.85
Novembruuo

Novembruuo

Beginner2021-11-22Added 26 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)=53x+1. Find its integral.
5ln(3x+1)304
Step 3: Since F(x)ab=F(b)F(a), expand the above into F(4)−F(0):
5ln(3×4+1)35ln(3×0+1)3
Step 4: Simplify.
5ln133

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