We have an answer to "Evaluate the definite integral. ∫36(−5x+6)dx"

Lorenzolaji

Answered question

2021-11-18

Evaluate the definite integral.

\int_{3}^{6} (- 5 x + 6) d x

Ryan Willis

Beginner2021-11-19Added 15 answers

Step 1
To evaluate the given definite integral.
Step 2
Given that:

\int_{3}^{6} (- 5 x + 6) d x

= - 5 {|_{{3}}^{6} x d x + 6 |}_{3}^{6} d x

= - 5 {[\frac{x^{2}}{2}]}_{3}^{6} + 6 {[x]}_{3}^{6}

= \frac{- 5}{2} [6^{2} - 3^{2}] + 6 [6 - 3]

= \frac{- 5}{2} (36 - 9) + 6 (3)

= \frac{- 5}{2} (27) + 18

= \frac{- 135}{2} + 18

= \frac{- 135 + 36}{2}

= \frac{- 99}{2}

∴ ∣_{3}^{6} (5 x + 6) d x = \frac{- 99}{2}

menerkupvd

Beginner2021-11-20Added 12 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)=(−5x+6). Find its integral.

- \frac{5 x^{2}}{2} + 6 x ∣_{3}^{6}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(6)-F(3):

(- \frac{5 \times 6^{2}}{2} + 6 \times 6) - (- \frac{5 \times 3^{2}}{2} + 6 \times 3)

Step 4: Simplify.

- \frac{99}{2}

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