What is the integral from 0 to 5 of (t^2+2t-15) ?

The integral from 0 to 5 of (t^2+2t-15) is -25/3

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integral from 0 to 5 of (t^2+2t-15)

\int_{0}^{5} (t^{2} + 2 t - 15) d t

- \frac{25}{3}

Decimal Notation

- 8.33333 \dots

Solution steps

\int_{0}^{5} t^{2} + 2 t - 15 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} 15 d t

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

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

\int_{0}^{5} 15 d t = 75

= \frac{125}{3} + 25 - 75

Simplify

\frac{125}{3} + 25 - 75 : - \frac{25}{3}

= - \frac{25}{3}

t \to 0 lim (\frac{5}{t} - \frac{5}{e ^{t} - 1})

y = x^{2} - 1, x = - 2, x = 1

\frac{d}{d x} (3 (4 - 9 x)^{4})

\int \frac{7 e ^{7 x}}{1 + e ^{7 x}} d x

What is the integral from 0 to 5 of (t^2+2t-15) ?
The integral from 0 to 5 of (t^2+2t-15) is -25/3