Find out the answer to "Evaluate the integral. ∫−84(−2x+8)dx"

High School
Calculus and Analysis
Calculus 2
Applications of integrals

interdicoxd

Answered question

2021-12-31

Evaluate the integral.

\int_{- 8}^{4} (- 2 x + 8) d x

Answer & Explanation

scomparve5j

Beginner2022-01-01Added 38 answers

Step 1
Given definite integral is:

\int_{- 8}^{4} (- 2 x + 8) d x

We have to evaluate the above definite integral.
Step 2
Then we get,

\int_{- 8}^{4} (- 2 x + 8) d x

= \int_{- 8}^{4} (- 2 x) d x + \int_{- 8}^{4} 8 d x

= - 2 \int_{- 8}^{4} x d x + 8 \int_{- 8}^{4} d x

= - 2 {[\frac{x^{2}}{2}]}_{- 8}^{4} + 8 {[x]}_{- 8}^{4}

= - 2 \times \frac{1}{2} \times [4^{2} - {(- 8)}^{2}] + 8 [4 - (- 8)]

=-(16-64)+8(4+8)
=-16+64+96
=144
Hence the answer.

kaluitagf

Beginner2022-01-02Added 38 answers

\int_{- 8}^{4} - 2 x + 8 d x

\int - 2 x + 8 d x

Use properties

- \int 2 x d x + \int 8 d x

Evaluate

- x^{2} + 8 x

Return the limits

(- x^{2} + 8 x) ∣_{- 8}^{4}

Calculate the expression

- 4^{2} + 8 \cdot 4 - (- {(- 8)}^{2} + 8 \cdot (- 8))

Answer:
144

Vasquez

Expert2022-01-07Added 669 answers

Step 1
Given
$\int (- 2 x + 8) d x$
Step 2
Solution:
$\int (- 2 x + 8) d x = - x^{2} + 8 x$
Let's calculate a definite integral:
$\int_{- 8}^{4} (- 2 x + 8) d x = (- x^{2} + 8 x) |_{- 8}^{4}$
F(4)=16
F(-8)=-128
I=16-(-128)=144
NSK
Answer:
144

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