What is the integral from 0 to 10 of 3x^2-42x+135 ?

The integral from 0 to 10 of 3x^2-42x+135 is 250

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integral from 0 to 10 of 3x^2-42x+135

\int_{0}^{10} 3 x^{2} - 42 x + 135 d x

250

Solution steps

\int_{0}^{10} 3 x^{2} - 42 x + 135 d x

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}^{10} 3 x^{2} d x - \int_{0}^{10} 42 x d x + \int_{0}^{10} 135 d x

\int_{0}^{10} 3 x^{2} d x = 1000

\int_{0}^{10} 42 x d x = 2100

\int_{0}^{10} 135 d x = 1350

= 1000 - 2100 + 1350

Simplify

= 250

\frac{d y}{d x}, y^{2} = x - y

f (x) = \frac{x ^{3} + 1}{x ^{2} + 1}

\int tan (u) d u

\frac{d y}{d x} x y = 4

x \to 2 lim (\frac{x ^{3} - 8}{x - 4})

What is the integral from 0 to 10 of 3x^2-42x+135 ?
The integral from 0 to 10 of 3x^2-42x+135 is 250