What is area 3x^2+6,y=6.4,y=8.1 ?

The answer to area 3x^2+6,y=6.4,y=8.1 is 2.14790…

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area 3x^2+6,y=6.4,y=8.1

area

3 x^{2} + 6, y = 6.4, y = 8.1

2.14790 \dots

Solution steps

To find the intersection points solve

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

6.4 = 8.1 :

False

6.4 = 3 x^{2} + 6 : x = \frac{3.33333 E 15}{2.5 E 16}, x = - \frac{3.33333 E 15}{2.5 E 16}

8.1 = 3 x^{2} + 6 : x = \frac{7}{10}, x = - \frac{7}{10}

= \int_{- \frac{7}{10}}^{- \frac{3.33333 E 15}{2.5 E 16}} ∣ f_{2} (x) - f_{3} (x) ∣ d x + \int_{- \frac{3.33333 E 15}{2.5 E 16}}^{\frac{3.33333 E 15}{2.5 E 16}} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{\frac{3.33333 E 15}{2.5 E 16}}^{\frac{7}{10}} ∣ f_{2} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{7}{10}}^{- \frac{3.33333 E 15}{2.5 E 16}} 8.1 - (3 x^{2} + 6) d x + \int_{- \frac{3.33333 E 15}{2.5 E 16}}^{\frac{3.33333 E 15}{2.5 E 16}} ∣ 6.4 - 8.1 ∣ d x + \int_{\frac{3.33333 E 15}{2.5 E 16}}^{\frac{7}{10}} 8.1 - (3 x^{2} + 6) d x

\int_{- \frac{7}{10}}^{- \frac{3.33333 E 15}{2.5 E 16}} 8.1 - (3 x^{2} + 6) d x = 0.45319 \dots

\int_{- \frac{3.33333 E 15}{2.5 E 16}}^{\frac{3.33333 E 15}{2.5 E 16}} ∣ 6.4 - 8.1 ∣ d x = 1.24150 \dots

\int_{\frac{3.33333 E 15}{2.5 E 16}}^{\frac{7}{10}} 8.1 - (3 x^{2} + 6) d x = 0.45319 \dots

= 0.45319 \dots + 1.24150 \dots + 0.45319 \dots

Simplify

= 2.14790 \dots

y = - 2 sin (x), at x = \frac{3}{4} π

\frac{d}{d x} (\frac{cos ( x )}{1 + cos ( x )})

n = 0 \sum \infty \frac{4 n}{- 4 n + 7}

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

f (x) = 30 + 10 e^{- 0.05 x}

What is area 3x^2+6,y=6.4,y=8.1 ?
The answer to area 3x^2+6,y=6.4,y=8.1 is 2.14790…