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Popular >

integral from 1 to 4 of (x-3)^2

Solution

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

Solution

3

Solution steps

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

Expand

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

= \int_{1}^{4} x^{2} - 6 x + 9 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} 6 x d x + \int_{1}^{4} 9 d x

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

\int_{1}^{4} 6 x d x = 45

\int_{1}^{4} 9 d x = 27

= 21 - 45 + 27

Simplify

= 3

Popular Examples

xy^'+y=8xy^2,y(1)=3

x y^{^{'}} + y = 8 x y^{2}, y (1) = 3

derivative of cos(2*x)

\frac{d}{d x} (cos (2 \cdot x))

tangent of y=8sqrt(x),(4,16)tangent of

y = 8 x, (4, 16)

(\partial)/(\partial x)((75-x) 1/3 pix^2)

\frac{\partial}{\partial x} ((75 - x) \frac{1}{3} π x^{2})

(\partial)/(\partial x)(xln(y)+1/9 x^3)

\frac{\partial}{\partial x} (x ln (y) + \frac{1}{9} x^{3})

Frequently Asked Questions (FAQ)

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