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Popular Calculus >

integral from 0 to 3 of (3-x)^2

Solution

\int_{0}^{3} (3 - x)^{2} d x

Solution

9

Solution steps

\int_{0}^{3} (3 - x)^{2} d x

Expand

(3 - x)^{2} : 9 - 6 x + x^{2}

= \int_{0}^{3} 9 - 6 x + x^{2} 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_{0}^{3} 9 d x - \int_{0}^{3} 6 x d x + \int_{0}^{3} x^{2} d x

\int_{0}^{3} 9 d x = 27

\int_{0}^{3} 6 x d x = 27

\int_{0}^{3} x^{2} d x = 9

= 27 - 27 + 9

Simplify

= 9

Graph

Popular Examples

y^{''}+5y^'+4y=8te^{2t}

y^{^{''}} + 5 y^{^{'}} + 4 y = 8 t e^{2 t}

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x \to + 0 + lim (3 x)

derivative of f(x)=x^2sqrt(4x-1)derivative of

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laplacetransform sin(5t-pi/3)*1(5t-pi/3)laplace transform

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inverse oflaplace (3z-5)/(z^2-4z+3)inverse laplace

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Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of (3-x)^2 ?
The integral from 0 to 3 of (3-x)^2 is 9