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Popular >

integral from 0 to 3 of t^2-t-6

Solution

\int_{0}^{3} t^{2} - t - 6 d t

Solution

- \frac{27}{2}

+1

Decimal Notation

- 13.5

Solution steps

\int_{0}^{3} t^{2} - t - 6 d t

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}^{3} t^{2} d t - \int_{0}^{3} t d t - \int_{0}^{3} 6 d t

\int_{0}^{3} t^{2} d t = 9

\int_{0}^{3} t d t = \frac{9}{2}

\int_{0}^{3} 6 d t = 18

= 9 - \frac{9}{2} - 18

Simplify

9 - \frac{9}{2} - 18 : - \frac{27}{2}

= - \frac{27}{2}

Popular Examples

integral from 0 to 2 of sqrt(x^2-2x+2)

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

integral from 6 to 36 of 1/(x(ln(x))^6)

\int_{6}^{36} \frac{1}{x ( ln ( x ) ) ^{6}} d x

integral from 0 to 1 of 1/4

\int_{0}^{1} \frac{1}{4} d x

integral from 1 to 7 of 9/x

\int_{1}^{7} \frac{9}{x} d x

integral from 1 to e of ln(x)-ln^2(x)

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

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of t^2-t-6 ?
The integral from 0 to 3 of t^2-t-6 is -27/2