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Popular >

integral of |2-x|

Solution

\int ∣ 2 - x ∣ d x

Solution

\frac{( - 2 + x ) ∣ - 2 + x ∣}{2} + C

Solution steps

\int ∣ 2 - x ∣ d x

Factor

2 - x : - (- 2 + x)

= \int ∣ - (- 2 + x) ∣ d x

Simplify

∣ - (- 2 + x) ∣ : ∣ - 2 + x ∣

= \int ∣ - 2 + x ∣ d x

Apply u-substitution

: \int ∣ u ∣ d u

= \int ∣ u ∣ d u

Use the common integral:

\int ∣ u ∣ d u = \frac{u ∣ u ∣}{2}

= \frac{u ∣ u ∣}{2}

Substitute back

u = - 2 + x

= \frac{( - 2 + x ) ∣ - 2 + x ∣}{2}

Add a constant to the solution

= \frac{( - 2 + x ) ∣ - 2 + x ∣}{2} + C

Popular Examples

integral of sqrt(sec(x))tan^5(x)

\int sec (x) tan^{5} (x) d x

integral of (3x+4)/((x^2+9))

\int \frac{3 x + 4}{( x ^{2} + 9 )} d x

integral of x/(2+3x^2)

\int \frac{x}{2 + 3 x ^{2}} d x

integral of sin^4(10x)+cos^4(10x)

\int sin^{4} (10 x) + cos^{4} (10 x) d x

integral of x^2e^{3x^2}

\int x^{2} e^{3 x^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of |2-x| ?
The integral of |2-x| is ((-2+x)|-2+x|)/2+C