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Popular >

integral from 1 to 4 of (|2-x|)/x

Solution

\int_{1}^{4} \frac{∣ 2 - x ∣}{x} d x

Solution

1

Solution steps

\int_{1}^{4} \frac{∣ 2 - x ∣}{x} d x

Eliminate Absolutes

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

\int_{1}^{2} \frac{2 - x}{x} d x = 2 ln (2) - 1

\int_{2}^{4} \frac{- 2 + x}{x} d x = - 2 ln (2) + 2

= 2 ln (2) - 1 - 2 ln (2) + 2

Simplify

2 ln (2) - 1 - 2 ln (2) + 2 : 1

= 1

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\int_{- 4}^{8} ∣ x ∣ d x

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integral from 0 to x of f(t)(x-t)

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integral from pi/3 to pi of 0.5-cos(x)

\int_{\frac{π}{3}}^{π} 0.5 - cos (x) d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 4 of (|2-x|)/x ?
The integral from 1 to 4 of (|2-x|)/x is 1