Solve the equation- -02 -x2-x-1-dx

∫_0^2(x^2 x+1)dx =[x^33 x^22+x]_0^2 =13(8 0) 12(4 0)+(2 0) =83 42+2 =83 2+2 =83 ...

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Definite Integral as Limit of Sum

Solve the equ...

Question

Solve the equation:-
$\int_{0}^{2} [x^{2} - x + 1] d x$

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Solution

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\int_{0}^{2}

x^{2}

1

\int_{0}^{2} (| x | + | x - 1 |) d x =

2 \frac{d y}{d x} + \frac{1}{x} = \frac{e^{y}}{x^{2}} .

x y \frac{d y}{d x} = \frac{1 + y^{2}}{1 + x^{2}} (1 + x + x^{2})

\frac{d y}{d x} - \frac{2 x y}{1 + x^{2}} = x^{2} + 1

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