What is the integral from 0 to 3 of (4x^2-2x+5) ?

The integral from 0 to 3 of (4x^2-2x+5) is 42

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integral from 0 to 3 of (4x^2-2x+5)

\int_{0}^{3} (4 x^{2} - 2 x + 5) d x

42

Solution steps

\int_{0}^{3} 4 x^{2} - 2 x + 5 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} 4 x^{2} d x - \int_{0}^{3} 2 x d x + \int_{0}^{3} 5 d x

\int_{0}^{3} 4 x^{2} d x = 36

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

\int_{0}^{3} 5 d x = 15

= 36 - 9 + 15

Simplify

= 42

\int_{0}^{2} 5 x e^{- x^{2}} d x

\int_{0}^{1} 3 x (4 x^{2} - 1)^{5} d x

\int_{0}^{1} x^{2} (3 x^{2}) d x

\int_{- 1}^{1} \frac{1}{1 + t ^{2}} d t

\int_{0}^{π} (1 - cos (2 x)) d x

What is the integral from 0 to 3 of (4x^2-2x+5) ?
The integral from 0 to 3 of (4x^2-2x+5) is 42