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Popular >

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

Solution

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

Solution

3

Solution steps

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

Expand

(x - 5)^{2} : x^{2} - 10 x + 25

= \int_{3}^{6} x^{2} - 10 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_{3}^{6} x^{2} d x - \int_{3}^{6} 10 x d x + \int_{3}^{6} 25 d x

\int_{3}^{6} x^{2} d x = 63

\int_{3}^{6} 10 x d x = 135

\int_{3}^{6} 25 d x = 75

= 63 - 135 + 75

Simplify

= 3

Popular Examples

4y^{''}-y=0,y(-2)=1,y^'(-2)=-1

4 y^{^{''}} - y = 0, y (- 2) = 1, y^{^{'}} (- 2) = - 1

y^{''}-y^'-6y=e^{3x}

y^{^{''}} - y^{^{'}} - 6 y = e^{3 x}

laplacetransform 1-e^{-5t}laplace transform

1 - e^{- 5 t}

derivative of 4x^2e^x derivative of

4 x^{2} e^{x}

integral of 1/(sqrt(x)+x\sqrt{x)}

\int \frac{1}{x + x x} d x

Frequently Asked Questions (FAQ)

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