What is the integral from 1 to 2 of 5x^2-4x+3 ?

The integral from 1 to 2 of 5x^2-4x+3 is 26/3

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integral from 1 to 2 of 5x^2-4x+3

\int_{1}^{2} 5 x^{2} - 4 x + 3 d x

\frac{26}{3}

Decimal

8.66666 \dots

Solution steps

\int_{1}^{2} 5 x^{2} - 4 x + 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} 5 x^{2} d x - \int_{1}^{2} 4 x d x + \int_{1}^{2} 3 d x

\int_{1}^{2} 5 x^{2} d x = \frac{35}{3}

\int_{1}^{2} 4 x d x = 6

\int_{1}^{2} 3 d x = 3

= \frac{35}{3} - 6 + 3

Simplify

\frac{35}{3} - 6 + 3 : \frac{26}{3}

= \frac{26}{3}

\int \frac{1}{x ^{2} + 10} d x

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 0, y (1) = 0, y^{^{'}} (1) = 2.5

\int \frac{12 x}{e ^{2} - e ^{2 y^{2}}} d x

\int \frac{1}{( 4 y ) ^{2}} d y

f (x) = 6 sin (4 x)

What is the integral from 1 to 2 of 5x^2-4x+3 ?
The integral from 1 to 2 of 5x^2-4x+3 is 26/3