What is the integral from 4 to 6 of (5/3 x-5) ?

The integral from 4 to 6 of (5/3 x-5) is 20/3

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integral from 4 to 6 of (5/3 x-5)

\int_{4}^{6} (\frac{5}{3} x - 5) d x

\frac{20}{3}

Decimal Notation

6.66666 \dots

Solution steps

\int_{4}^{6} \frac{5}{3} x - 5 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_{4}^{6} \frac{5}{3} x d x - \int_{4}^{6} 5 d x

\int_{4}^{6} \frac{5}{3} x d x = \frac{50}{3}

\int_{4}^{6} 5 d x = 10

= \frac{50}{3} - 10

Simplify

\frac{50}{3} - 10 : \frac{20}{3}

= \frac{20}{3}

\int_{- 1}^{5} 4 x^{3} - 3 x^{2} + 1 d x

\int_{1}^{4} \frac{1}{( x - 3 ) ^{\frac{1}{5}}} d x

\int_{0}^{\frac{π}{6}} x cos (x + \frac{π}{3}) d x

\int_{1}^{e} ln (x^{4}) d x

\int_{0}^{3} x^{2} - 6 x + 8 d x

What is the integral from 4 to 6 of (5/3 x-5) ?
The integral from 4 to 6 of (5/3 x-5) is 20/3