What is the integral from 0 to 8 of 3t^2-36t+105 ?

The integral from 0 to 8 of 3t^2-36t+105 is 200

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integral from 0 to 8 of 3t^2-36t+105

\int_{0}^{8} 3 t^{2} - 36 t + 105 d t

200

Solution steps

\int_{0}^{8} 3 t^{2} - 36 t + 105 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}^{8} 3 t^{2} d t - \int_{0}^{8} 36 t d t + \int_{0}^{8} 105 d t

\int_{0}^{8} 3 t^{2} d t = 512

\int_{0}^{8} 36 t d t = 1152

\int_{0}^{8} 105 d t = 840

= 512 - 1152 + 840

Simplify

= 200

x \to 1 lim (g (x))

\int e^{- \frac{1}{2} x} d x

x \to - 1 lim (H (x))

\frac{d y}{d x} = 0.0019 y (3000 - y)

\frac{d}{d x} (x^{2} - 1)

What is the integral from 0 to 8 of 3t^2-36t+105 ?
The integral from 0 to 8 of 3t^2-36t+105 is 200