Question

Integrals upper limit 5 lower limit -5 |x+2|

Answer 1

Greetings,
The answer to your question is typed below↓
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Given:

∫(x+2) dx [upper limit = 5 & lower limit = -5]
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Solution:

1) Evaluate the definite integral

⇒ ∫ ( x^1 + 2) dx  [with upper limit = 5 & lower limit = -5]

2) The derivative of a polynomial is the sum of the anti derivative of its terms. The anti derivative of any constant term is cx. The anti derivative of ax^n is a/(n+1) * x^(n+1) .

⇒ 1/(1+1) * x^(1+1) + 2x + C

Simplifying we get:

⇒ 1/2 x² + 2x + C

3) The definite integral of a polynomial is the anti derivative of the polynomial evaluated a the upper limit of integration minus anti derivative of the polynomial evaluated a the lower limit of integration.

⇒ 1/2 * 5² + 2*5 - [ 1/2 * (-5)² + 2 * (-5)] 

Simplifying we get:

⇒ 45/2 - 45/2

4) Subtract 45/2 from 45/2 by finding a common denominator and subtracting the numerators. Then reduce the fraction to the lowest terms possible.

⇒ (45 -45)/2
⇒0

5) Final answer = 20.
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Ps: Enjoy ;)