What is the integral from 0 to 3 of 53-(3x^2+2x+20) ?

The integral from 0 to 3 of 53-(3x^2+2x+20) is 63

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integral from 0 to 3 of 53-(3x^2+2x+20)

\int_{0}^{3} 53 - (3 x^{2} + 2 x + 20) d x

63

Solution steps

\int_{0}^{3} 53 - (3 x^{2} + 2 x + 20) d x

Simplify

= \int_{0}^{3} - 3 x^{2} - 2 x + 33 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}^{3} 3 x^{2} d x - \int_{0}^{3} 2 x d x + \int_{0}^{3} 33 d x

\int_{0}^{3} 3 x^{2} d x = 27

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

\int_{0}^{3} 33 d x = 99

= - 27 - 9 + 99

Simplify

= 63

\int_{1}^{3} \frac{x}{2} d x

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

\int_{0.25}^{1.25} e^{- 4 x^{2}} d x

\int_{0}^{2} \frac{1}{2} e^{- \frac{x}{2}} d x

\int_{0}^{1} 5 x (x^{2} - 1)^{5} d x

What is the integral from 0 to 3 of 53-(3x^2+2x+20) ?
The integral from 0 to 3 of 53-(3x^2+2x+20) is 63