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Popular Calculus >

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

Solution

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

Solution

1

Solution steps

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

Expand

(3 x - 5)^{2} : 9 x^{2} - 30 x + 25

= \int_{1}^{2} 9 x^{2} - 30 x + 25 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} 9 x^{2} d x - \int_{1}^{2} 30 x d x + \int_{1}^{2} 25 d x

\int_{1}^{2} 9 x^{2} d x = 21

\int_{1}^{2} 30 x d x = 45

\int_{1}^{2} 25 d x = 25

= 21 - 45 + 25

Simplify

= 1

Graph

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Frequently Asked Questions (FAQ)

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