Area of the region between the graphs of y = 4*(x - 6)^2/3 + 2, y = 3*x^2/4 - 9*x + 29 from x = 4 to x = 6

The calculator will try to find the area bounded by $$$y = \frac{4 \left(x - 6\right)^{2}}{3} + 2$$$, $$$y = \frac{3 x^{2}}{4} - 9 x + 29$$$ from $$$x = 4$$$ to $$$x = 6$$$, with steps shown.

Curves:

Comma-separated. x-axis is $$$y = 0$$$, y-axis is $$$x = 0$$$.

Lower limit:

Optional.

Upper limit:

Optional.

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Your Input

Find the area of the region bounded by the curves $$$y = \frac{4 \left(x - 6\right)^{2}}{3} + 2$$$, $$$y = \frac{3 x^{2}}{4} - 9 x + 29$$$ from $$$x = 4$$$ to $$$x = 6$$$.

Solution

$$$\int\limits_{4}^{6} \left(\left(\frac{4 x \left(x - 12\right)}{3} + 50\right) - \left(\frac{3 x \left(x - 12\right)}{4} + 29\right)\right)\, dx = \frac{14}{9}\approx 1.555555555555556$$$

Total area: $$$A = \frac{14}{9}$$$.

Region bounded by y = 4*(x - 6)^2/3 + 2, y = 3*x^2/4 - 9*x + 29, x = 4, x = 6

Answer

Total area: $$$A = \frac{14}{9}\approx 1.555555555555556$$$A.

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Area of the region between the graphs of $$$y = \frac{4 \left(x - 6\right)^{2}}{3} + 2$$$, $$$y = \frac{3 x^{2}}{4} - 9 x + 29$$$ from $$$x = 4$$$ to $$$x = 6$$$

Your Input

Solution

Answer