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Popular >

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

Solution

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

Solution

3

Solution steps

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

Expand

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

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

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

\int_{1}^{4} 4 x d x = 30

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

= 21 - 30 + 12

Simplify

= 3

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\int cos (3 x) d x

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(x + 1)^{2}

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\int \frac{- x ^{2} cos ( x )}{4} d x

(\partial)/(\partial x)(ln(x^3+y^2)-z)

\frac{\partial}{\partial x} (ln (x^{3} + y^{2}) - z)

derivative of y=x^{8x}derivative of

y = x^{8 x}

Frequently Asked Questions (FAQ)

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