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Popular Calculus >

integral from-2 to 7 of |x-2|

Solution

\int_{- 2}^{7} ∣ x - 2 ∣ d x

Solution

\frac{41}{2}

+1

Decimal

20.5

Solution steps

\int_{- 2}^{7} ∣ x - 2 ∣ d x

Eliminate Absolutes

= \int_{- 2}^{2} - x + 2 d x + \int_{2}^{7} x - 2 d x

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

\int_{2}^{7} x - 2 d x = \frac{25}{2}

= 8 + \frac{25}{2}

Simplify

8 + \frac{25}{2} : \frac{41}{2}

= \frac{41}{2}

Graph

Popular Examples

integral from-3 to 2 of 3|x|

\int_{- 3}^{2} 3 ∣ x ∣ d x

integral from 0 to 1 of (3-8x^3+16x^7)

\int_{0}^{1} (3 - 8 x^{3} + 16 x^{7}) d x

integral from 3 to 10 of ln(x)

\int_{3}^{10} ln (x) d x

integral from-1 to 1 of 5/8 x(1-x^4)

\int_{- 1}^{1} \frac{5}{8} x (1 - x^{4}) d x

integral from 4 to 12 of xsqrt(1+x^2)

\int_{4}^{12} x 1 + x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral from-2 to 7 of |x-2| ?
The integral from-2 to 7 of |x-2| is 41/2