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

The integral from 2 to 3 of (x-4)^2 is 7/3

Popular >

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

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

\frac{7}{3}

Decimal

2.33333 \dots

Solution steps

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

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int_{2}^{3} x^{2} - 8 x + 16 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_{2}^{3} x^{2} d x - \int_{2}^{3} 8 x d x + \int_{2}^{3} 16 d x

\int_{2}^{3} x^{2} d x = \frac{19}{3}

\int_{2}^{3} 8 x d x = 20

\int_{2}^{3} 16 d x = 16

= \frac{19}{3} - 20 + 16

Simplify

\frac{19}{3} - 20 + 16 : \frac{7}{3}

= \frac{7}{3}

\int_{0}^{0.1} 1 d x

\int_{0}^{2} cos (x^{2}) x d x

\int_{- 1}^{1} \frac{5}{x ^{6}} d x

\int_{0}^{\frac{1}{4}} \frac{1}{1 - x ^{2}} d x

\int_{x}^{1} \frac{6}{7} x + \frac{12}{7} y d y

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