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Popular >

integral from 5 to 8 of (x-7)^2

Solution

\int_{5}^{8} (x - 7)^{2} d x

Solution

3

Solution steps

\int_{5}^{8} (x - 7)^{2} d x

Expand

(x - 7)^{2} : x^{2} - 14 x + 49

= \int_{5}^{8} x^{2} - 14 x + 49 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_{5}^{8} x^{2} d x - \int_{5}^{8} 14 x d x + \int_{5}^{8} 49 d x

\int_{5}^{8} x^{2} d x = 129

\int_{5}^{8} 14 x d x = 273

\int_{5}^{8} 49 d x = 147

= 129 - 273 + 147

Simplify

= 3

Popular Examples

(dy)/(dx)= 1/(y^3)

\frac{d y}{d x} = \frac{1}{y ^{3}}

limit as x approaches-2+of (x+1)/(x+2)

x \to - 2 + lim (\frac{x + 1}{x + 2})

integral of 1/(xsqrt(4x^2-16))

\int \frac{1}{x 4 x ^{2} - 16} d x

tangent of y=7+5x^2-2x^3,(2,11)tangent of

y = 7 + 5 x^{2} - 2 x^{3}, (2, 11)

limit as x approaches 2 of (x+4)/(x-2)

x \to 2 lim (\frac{x + 4}{x - 2})

Frequently Asked Questions (FAQ)

What is the integral from 5 to 8 of (x-7)^2 ?
The integral from 5 to 8 of (x-7)^2 is 3