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andriy [413]
3 years ago
11

Find the area of the shaded region.f(x)=4x+3x2−x3,g(x)=0 The area is _____.

Mathematics
1 answer:
Tasya [4]3 years ago
7 0

Answer:

The answer is " \bold{\frac{7}{2}}"

Step-by-step explanation:

Given value:

\to f(x)=4x+3x^2-x^3\\\\\to g(x)=0

Find:

area=?

calculation:

\ Area = \int_{-1}^{0} -(4x+3x^2-x^3) dx  + \int_{0}^{1} (4x+3x^2-x^3) dx  \\\\

        =  -(2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\=  -( 2x^2+x^3- \frac{x^4}{4})_{-1}^{0} + (2x^2+x^3- \frac{x^4}{4})_{0}^{1}\\\\\\= ( 2- 1 -\frac{1}{4}) + (2+1- \frac{1}{4})\\\\\\=  ( \frac{8-4-1}{4}) + (\frac{8+4-1}{4})\\\\=  ( \frac{3}{4}) + (\frac{11}{4})\\\\=   \frac{3}{4} + \frac{11}{4}\\\\= \frac{11+3}{4}\\\\= \frac{14}{4}\\\\= \frac{7}{2}\\\\

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