What is the integral from 0 to 5 of t^2+2t-3 ?

The integral from 0 to 5 of t^2+2t-3 is 155/3

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integral from 0 to 5 of t^2+2t-3

\int_{0}^{5} t^{2} + 2 t - 3 d t

\frac{155}{3}

Decimal Notation

51.66666 \dots

Solution steps

\int_{0}^{5} 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_{0}^{5} t^{2} d t + \int_{0}^{5} 2 t d t - \int_{0}^{5} 3 d t

\int_{0}^{5} t^{2} d t = \frac{125}{3}

\int_{0}^{5} 2 t d t = 25

\int_{0}^{5} 3 d t = 15

= \frac{125}{3} + 25 - 15

Simplify

\frac{125}{3} + 25 - 15 : \frac{155}{3}

= \frac{155}{3}

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\int_{0}^{- 5} (\frac{2}{5} x^{2} + 2 x - 2) d x

What is the integral from 0 to 5 of t^2+2t-3 ?
The integral from 0 to 5 of t^2+2t-3 is 155/3