What is the integral from 3 to 4 of (t^2-2t-3) ?

The integral from 3 to 4 of (t^2-2t-3) is 7/3

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integral from 3 to 4 of (t^2-2t-3)

\int_{3}^{4} (t^{2} - 2 t - 3) d t

\frac{7}{3}

Decimal

2.33333 \dots

Solution steps

\int_{3}^{4} t^{2} - 2 t - 3 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_{3}^{4} t^{2} d t - \int_{3}^{4} 2 t d t - \int_{3}^{4} 3 d t

\int_{3}^{4} t^{2} d t = \frac{37}{3}

\int_{3}^{4} 2 t d t = 7

\int_{3}^{4} 3 d t = 3

= \frac{37}{3} - 7 - 3

Simplify

\frac{37}{3} - 7 - 3 : \frac{7}{3}

= \frac{7}{3}

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What is the integral from 3 to 4 of (t^2-2t-3) ?
The integral from 3 to 4 of (t^2-2t-3) is 7/3