What is the integral from 1 to 4 of (3x^2-2x+4) ?

The integral from 1 to 4 of (3x^2-2x+4) is 60

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integral from 1 to 4 of (3x^2-2x+4)

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

60

Solution steps

\int_{1}^{4} 3 x^{2} - 2 x + 4 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_{1}^{4} 3 x^{2} d x - \int_{1}^{4} 2 x d x + \int_{1}^{4} 4 d x

\int_{1}^{4} 3 x^{2} d x = 63

\int_{1}^{4} 2 x d x = 15

\int_{1}^{4} 4 d x = 12

= 63 - 15 + 12

Simplify

= 60

\int_{1}^{2} e^{x} + 2 d x

\int_{1}^{2} \frac{3 x - y}{9} d y

\int_{0}^{0.5} \frac{1}{1 - x} d x

\int_{3}^{15} \frac{( 5 x ^{2} - 9 )}{3} d x

\int_{0}^{3} 1 + 36 x^{2} d x

What is the integral from 1 to 4 of (3x^2-2x+4) ?
The integral from 1 to 4 of (3x^2-2x+4) is 60