What is the integral from 1 to 7 of t^2-4t-12 ?

The integral from 1 to 7 of t^2-4t-12 is -54

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integral from 1 to 7 of t^2-4t-12

\int_{1}^{7} t^{2} - 4 t - 12 d t

- 54

Solution steps

\int_{1}^{7} t^{2} - 4 t - 12 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_{1}^{7} t^{2} d t - \int_{1}^{7} 4 t d t - \int_{1}^{7} 12 d t

\int_{1}^{7} t^{2} d t = 114

\int_{1}^{7} 4 t d t = 96

\int_{1}^{7} 12 d t = 72

= 114 - 96 - 72

Simplify

= - 54

\frac{d}{d t} (cosh^{2} (t))

\frac{d y}{d x} = \frac{y ^{2} + 2 x x ^{2} + y ^{2}}{x y}

x \to \infty lim (2 x + 2)

(t^{2})^{^{'}}

f (x) = x^{2} - x - ln (x)

What is the integral from 1 to 7 of t^2-4t-12 ?
The integral from 1 to 7 of t^2-4t-12 is -54