Expert answers to "Evaluate the definite integral. ∫146x+2dx"

chanyingsauu7

Answered question

2021-11-17

Evaluate the definite integral.

\int_{1}^{4} 6 x + 2 d x

Geraldine Flores

Beginner2021-11-18Added 21 answers

Step 1
the objective is to evaluate the integral.
Step 2
Solution:

\int_{1}^{4} 6 x + 2 d x

= {[6 \frac{x^{2}}{2} + 2 x]}_{1}^{4}

= \frac{6 {(4)}^{2}}{2} + 2 (4) - \frac{6 {(1)}^{2}}{2} - 2 (1)

= \frac{96}{2} + 8 - \frac{6}{2} - 2

= \frac{96 + 16 - 6 - 4}{2}

= \frac{102}{2} = 51

\int_{1}^{4} (6 x + 2) d x = 51

Kathleen Ashton

Beginner2021-11-19Added 15 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)=6x+2. Find its integral.

3 x^{2} = 2 x ∣_{1}^{4}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(4)−F(1):

(3 \times 4^{2} + 2 \times 4) - (3 \times 1^{2} + 2 \times 1)

Step 4: Simplify.
=51

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