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Popular >

integral from 4 to 7 of (x-6)^2

Solution

\int_{4}^{7} (x - 6)^{2} d x

Solution

3

Solution steps

\int_{4}^{7} (x - 6)^{2} d x

Expand

(x - 6)^{2} : x^{2} - 12 x + 36

= \int_{4}^{7} x^{2} - 12 x + 36 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_{4}^{7} x^{2} d x - \int_{4}^{7} 12 x d x + \int_{4}^{7} 36 d x

\int_{4}^{7} x^{2} d x = 93

\int_{4}^{7} 12 x d x = 198

\int_{4}^{7} 36 d x = 108

= 93 - 198 + 108

Simplify

= 3

Popular Examples

limit as x approaches 5 of (x^2-9)/(x-3)

x \to 5 lim (\frac{x ^{2} - 9}{x - 3})

y^{^{'}} - 2 y = 4

derivative of sin(tan(e^{x^2}))derivative of

sin (tan (e^{x^{2}}))

integral of 1/((s^2+1)^3)

\int \frac{1}{( s ^{2} + 1 ) ^{3}} d s

y^{''}-4y^'+5y=0,y(0)=1,y^'(0)=-1

y^{^{''}} - 4 y^{^{'}} + 5 y = 0, y (0) = 1, y^{^{'}} (0) = - 1

Frequently Asked Questions (FAQ)

What is the integral from 4 to 7 of (x-6)^2 ?
The integral from 4 to 7 of (x-6)^2 is 3