Mathematics, 10.07.2019 03:00 gonzalesalexiaouv1bg
Find the area between the curves: y=x3−14x2+45x and y=−x3+14x2−45x
Answers: 1
![2\left(\int\limits_{-9}^{-5}(x^3+14x^2+45x)dx-\int\limits_{-5}^0(x^3+14x^2+45x)dx\right)=(*)\\\\\int(x^3+14x^2+45x)dx=\dfrac{1}{4}x^4+\dfrac{14}{3}x^3+\dfrac{45}{2}x^2\\\\\int\limits_{-9}^{-5}(x^3+14x^2+45x)dx=\left\dfrac{1}{4}x^4+\dfrac{14}{3}x^3+\dfrac{45}{2}x^2\right]_{-9}^{-5}\\\\=\left(\dfrac{1}{4}(-5)^4+\dfrac{14}{3}(-5)^3+\dfrac{45}{2}(-5)^2\right)-\left(\dfrac{1}{4}(-9)^4+\dfrac{14}{3}(-9)^3+\dfrac{45}{2}(-9)^2\right)\\\\=\dfrac{224}{3}](/tpl/images/0071/7503/6bf97.png)
![\int\limits_{-5}^{0}(x^3+14x^2+45x)dx=\left\dfrac{1}{4}x^4+\dfrac{14}{3}x^3+\dfrac{45}{2}x^2\right]_{-5}^{0}\\\\=\left(\dfrac{1}{4}0^4+\dfrac{14}{3}0^3+\dfrac{45}{2}0^2\right)-\left(\dfrac{1}{4}(-5)^4+\dfrac{14}{3}(-5)^3+\dfrac{45}{2}(-5)^2\right)\\\\=-\dfrac{1625}{12}](/tpl/images/0071/7503/75413.png)
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Find the area between the curves: y=x3−14x2+45x and y=−x3+14x2−45x...
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