What is area y=-x^2+3x+1,y=-x+1 ?

The answer to area y=-x^2+3x+1,y=-x+1 is 32/3

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area y=-x^2+3x+1,y=-x+1

area

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

\frac{32}{3}

Solution steps

Apply the area formula:

\int_{0}^{4} - x^{2} + 3 x + 1 - (- x + 1) d x

Solve

\int_{0}^{4} - x^{2} + 3 x + 1 - (- x + 1) d x : \frac{32}{3}

The area is:

= \frac{32}{3}

x \to 0 lim (- 22)

\int \frac{( x e ^{2 x} )}{( 2 x + 1 ) ^{2}} d x

x \to 0 lim (\frac{( x ^{2} - x )}{x})

\int cos (2 x - 1) d x

\int_{1}^{1.5} x^{2} ln (x) d x