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Popular Calculus >

integral from 0 to 2 of x^2-5x+6

Solution

\int_{0}^{2} x^{2} - 5 x + 6 d x

Solution

\frac{14}{3}

+1

Decimal

4.66666 \dots

Solution steps

\int_{0}^{2} x^{2} - 5 x + 6 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_{0}^{2} x^{2} d x - \int_{0}^{2} 5 x d x + \int_{0}^{2} 6 d x

\int_{0}^{2} x^{2} d x = \frac{8}{3}

\int_{0}^{2} 5 x d x = 10

\int_{0}^{2} 6 d x = 12

= \frac{8}{3} - 10 + 12

Simplify

\frac{8}{3} - 10 + 12 : \frac{14}{3}

= \frac{14}{3}

Graph

Popular Examples

integral from 0 to pi/2 of 1/(3+2cos(x))

\int_{0}^{\frac{π}{2}} \frac{1}{3 + 2 cos ( x )} d x

integral from 0 to pi/4 of arctan(x)

\int_{0}^{\frac{π}{4}} arctan (x) d x

integral from 3 to 6 of x^2-6x+9

\int_{3}^{6} x^{2} - 6 x + 9 d x

integral from 0 to 2x of e^{t^2}

\int_{0}^{2 x} e^{t^{2}} d t

integral from pi/6 to pi/4 of sin(x)

\int_{\frac{π}{6}}^{\frac{π}{4}} sin (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of x^2-5x+6 ?
The integral from 0 to 2 of x^2-5x+6 is 14/3