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

The integral from 0 to 3 of (t^2+2t-3) is 9

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integral from 0 to 3 of (t^2+2t-3)

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

9

Solution steps

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

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

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

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

= 9 + 9 - 9

Simplify

= 9

\int_{- 1}^{3} (2 x - 1) d x

\int_{- 1}^{2} ∣ 2 x - 1 ∣ d x

\int_{- 1}^{1} \frac{x}{2 + x ^{2}} d x

\int_{- 7}^{1} (- x^{2} - 3 x) d x

\int_{0}^{\frac{1}{2}} \frac{1}{x ( ln ( x ) ) ^{2}} d x

What is the integral from 0 to 3 of (t^2+2t-3) ?
The integral from 0 to 3 of (t^2+2t-3) is 9