What is area 6x-2,x^2+2x+2,1 ?

The answer to area 6x-2,x^2+2x+2,1 is 9/4

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area 6x-2,x^2+2x+2,1

area

6 x - 2, x^{2} + 2 x + 2, 1

\frac{9}{4}

Decimal Notation

2.25

Solution steps

To find the intersection points solve

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

6 x - 2 = x^{2} + 2 x + 2 : x = 2

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

x^{2} + 2 x + 2 = 1 : x = - 1

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

= \int_{- 1}^{\frac{1}{2}} x^{2} + 2 x + 2 - 1 d x + \int_{\frac{1}{2}}^{2} 6 x - 2 - (x^{2} + 2 x + 2) d x

\int_{- 1}^{\frac{1}{2}} x^{2} + 2 x + 2 - 1 d x = \frac{9}{8}

\int_{\frac{1}{2}}^{2} 6 x - 2 - (x^{2} + 2 x + 2) d x = \frac{9}{8}

= \frac{9}{8} + \frac{9}{8}

Simplify

= \frac{9}{4}

(- 1, 3), (- 6, - 2)

\int (2 + cos (2 x))^{2} d x

\int_{- 1}^{2} (2 - x^{2}) - (- x) d x

\frac{\partial}{\partial y} (- 0.27 y^{2} + 3.78 y)

y = \frac{f ( x )}{x ^{4}}