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Popular >

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

Solution

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

Solution

9

Solution steps

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

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{1}^{4} x^{2} - 8 x + 16 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} x^{2} d x - \int_{1}^{4} 8 x d x + \int_{1}^{4} 16 d x

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 8 x d x = 60

\int_{1}^{4} 16 d x = 48

= 21 - 60 + 48

Simplify

= 9

Graph

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\int_{- 1}^{x} t^{5} d t

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\int_{0}^{3} 1 - e^{- 2 x} d x

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integral from 0 to pi/2 of 1/2 cos(x)

\int_{0}^{\frac{π}{2}} \frac{1}{2} cos (x) d x

integral from-2 to 1 of 3x+4

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

Frequently Asked Questions (FAQ)

What is the integral from 1 to 4 of (x-4)^2 ?
The integral from 1 to 4 of (x-4)^2 is 9