What is area y=sqrt(x+2),y=2,y= 1/(x+1) ?

The answer to area y=sqrt(x+2),y=2,y= 1/(x+1) is 0.80453…

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area y=sqrt(x+2),y=2,y= 1/(x+1)

area

y = x + 2, y = 2, y = \frac{1}{x + 1}

0.80453 \dots

Solution steps

To find the intersection points solve

f_{i} (x) = f_{j} (x)

x + 2 = 2 : x = 2

x + 2 = \frac{1}{x + 1} : x \approx - 0.24512 \dots

2 = \frac{1}{x + 1} : x = - \frac{1}{2}

= \int_{- \frac{1}{2}}^{- 0.24512 \dots} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- 0.24512 \dots}^{2} ∣ f_{1} (x) - f_{2} (x) ∣ d x

= \int_{- \frac{1}{2}}^{- 0.24512 \dots} 2 - \frac{1}{x + 1} d x + \int_{- 0.24512 \dots}^{2} x + 2 - 2 d x

\int_{- \frac{1}{2}}^{- 0.24512 \dots} 2 - \frac{1}{x + 1} d x = 0.09780 \dots

\int_{- 0.24512 \dots}^{2} x + 2 - 2 d x = 0.70672 \dots

= 0.09780 \dots + 0.70672 \dots

Simplify

= 0.80453 \dots

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\frac{d}{d x} (ln (3 + 2 x))

x \to 1 lim (x^{2} + 1)

What is area y=sqrt(x+2),y=2,y= 1/(x+1) ?
The answer to area y=sqrt(x+2),y=2,y= 1/(x+1) is 0.80453…