Question

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

Answer 1

The answer is "
`\bold{(7)/(2)}`"

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- (x^4)/(4))_(-1)^(0) + (2x^2+x^3- (x^4)/(4))_(0)^(1)\\\\\\= -( 2x^2+x^3- (x^4)/(4))_(-1)^(0) + (2x^2+x^3- (x^4)/(4))_(0)^(1)\\\\\\= ( 2- 1 -(1)/(4)) + (2+1- (1)/(4))\\\\\\= ( (8-4-1)/(4)) + ((8+4-1)/(4))\\\\= ( (3)/(4)) + ((11)/(4))\\\\= (3)/(4) + (11)/(4)\\\\= (11+3)/(4)\\\\= (14)/(4)\\\\= (7)/(2)\\\\`