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Popular >

integral from 0 to 3 of |3t-5|

Solution

\int_{0}^{3} ∣ 3 t - 5 ∣ d t

Solution

\frac{41}{6}

+1

Decimal Notation

6.83333 \dots

Solution steps

\int_{0}^{3} ∣ 3 t - 5 ∣ d t

Eliminate Absolutes

= \int_{0}^{\frac{5}{3}} - 3 t + 5 d t + \int_{\frac{5}{3}}^{3} 3 t - 5 d t

\int_{0}^{\frac{5}{3}} - 3 t + 5 d t = \frac{25}{6}

\int_{\frac{5}{3}}^{3} 3 t - 5 d t = \frac{8}{3}

= \frac{25}{6} + \frac{8}{3}

Simplify

\frac{25}{6} + \frac{8}{3} : \frac{41}{6}

= \frac{41}{6}

Popular Examples

integral from-pi to pi of cos(n)x

\int_{- π}^{π} cos (n) x d x

integral from 1 to 5 of (z^2+4)/z

\int_{1}^{5} \frac{z ^{2} + 4}{z} d z

integral from 0.5 to 1 of x^4

\int_{0.5}^{1} x^{4} d x

integral from 0 to 2 of 12x^3+3x^2-4x

\int_{0}^{2} 12 x^{3} + 3 x^{2} - 4 x d x

integral from 0 to 5 of sqrt(|x^2-9|)

\int_{0}^{5} ∣ x^{2} - 9 ∣ d x

Frequently Asked Questions (FAQ)

What is the integral from 0 to 3 of |3t-5| ?
The integral from 0 to 3 of |3t-5| is 41/6