What is the integral from (-8)/7 to 8/11 of 7/4 x+2 ?

The integral from (-8)/7 to 8/11 of 7/4 x+2 is 2592/847

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integral from (-8)/7 to 8/11 of 7/4 x+2

\int_{\frac{- 8}{7}}^{\frac{8}{11}} \frac{7}{4} x + 2 d x

\frac{2592}{847}

Decimal Notation

3.06021 \dots

Solution steps

\int_{\frac{- 8}{7}}^{\frac{8}{11}} \frac{7}{4} x + 2 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_{\frac{- 8}{7}}^{\frac{8}{11}} \frac{7}{4} x d x + \int_{\frac{- 8}{7}}^{\frac{8}{11}} 2 d x

\int_{\frac{- 8}{7}}^{\frac{8}{11}} \frac{7}{4} x d x = - \frac{576}{847}

\int_{\frac{- 8}{7}}^{\frac{8}{11}} 2 d x = \frac{288}{77}

= - \frac{576}{847} + \frac{288}{77}

Simplify

- \frac{576}{847} + \frac{288}{77} : \frac{2592}{847}

= \frac{2592}{847}

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\int_{1}^{2} \frac{I n x}{x} d x

What is the integral from (-8)/7 to 8/11 of 7/4 x+2 ?
The integral from (-8)/7 to 8/11 of 7/4 x+2 is 2592/847