What is area x^2+2x+1,2x+5,-2,2 ?

The answer to area x^2+2x+1,2x+5,-2,2 is 32/3

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area x^2+2x+1,2x+5,-2,2

area

x^{2} + 2 x + 1, 2 x + 5, - 2, 2

\frac{32}{3}

Decimal Notation

10.66666 \dots

Solution steps

Apply the area formula:

\int_{- 2}^{2} x^{2} + 2 x + 1 - (2 x + 5) d x

Solve

\int_{- 2}^{2} x^{2} + 2 x + 1 - (2 x + 5) d x : \frac{32}{3}

The area is:

= \frac{32}{3}

\int x^{2} + 4 x + 5 d x

y d y = 4 x y^{2} + 1 d x

\frac{d y}{d x} = \frac{x ^{2} + y ^{2}}{x ^{2}}

(\frac{x}{x ^{2} + y ^{4}}) d x + (\frac{( 2 y ^{3} )}{x ^{2} + y ^{4}}) d y = 0

\frac{d}{d x} (\frac{7 x ^{3} + x}{6 x})