What is the integral from 1 to 2 of (6x^5-3x^2+2x) ?

The integral from 1 to 2 of (6x^5-3x^2+2x) is 59

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integral from 1 to 2 of (6x^5-3x^2+2x)

\int_{1}^{2} (6 x^{5} - 3 x^{2} + 2 x) d x

59

Solution steps

\int_{1}^{2} 6 x^{5} - 3 x^{2} + 2 x 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}^{2} 6 x^{5} d x - \int_{1}^{2} 3 x^{2} d x + \int_{1}^{2} 2 x d x

\int_{1}^{2} 6 x^{5} d x = 63

\int_{1}^{2} 3 x^{2} d x = 7

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

= 63 - 7 + 3

Simplify

= 59

\int_{y}^{1} 3 y d y

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

\int_{- 1}^{1} \frac{6}{x ^{2} + 1} d x

\int_{2}^{4} 2^{5 x} d x

\int_{\frac{π}{3}}^{π} cos (x) d x

What is the integral from 1 to 2 of (6x^5-3x^2+2x) ?
The integral from 1 to 2 of (6x^5-3x^2+2x) is 59