"Evaluate the definite integral. ∫0453x+1dx" was answered by our experts

scottyqegi

Answered question

2021-11-20

Evaluate the definite integral.

\int_{0}^{4} \frac{5}{3 x + 1} d x

George Blue

Beginner2021-11-21Added 18 answers

Step 1
we have the integral

\int_{0}^{4} \frac{5}{3 x + 1} d x

we will use the formula

\int \frac{1}{a x + b} d x = \frac{1}{a} \log (a x + b) + c

Step 2
integrating it we get

{[\frac{5}{3} \log (3 x + 1)]}_{0}^{4}

= (\frac{5}{3} \log (3 (4) + 1)) - (\frac{5}{3} \log (3 (0) + 1))

= (\frac{5}{3} \log (13)) - (\frac{5}{3} \log (1))

= \frac{5}{3} \log (\frac{13}{1})

= \frac{5}{3} (1.11)

=1.85
Step 3
hence the value is 1.85

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:

\int_{a}^{b} f (x) d x = F (x) ∣_{a}^{b} = F (b) - F (a)

Step 2: In this case,

f (x) = \frac{5}{3 x + 1}

. Find its integral.

\frac{5 \ln (3 x + 1)}{3} ∣_{0}^{4}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(4)−F(0):

\frac{5 \ln (3 \times 4 + 1)}{3} - \frac{5 \ln (3 \times 0 + 1)}{3}

Step 4: Simplify.

\frac{5 \ln 13}{3}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?