What is the integral from 0 to 1 of 5-(-3/2 x+4) ?

The integral from 0 to 1 of 5-(-3/2 x+4) is 7/4

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integral from 0 to 1 of 5-(-3/2 x+4)

\int_{0}^{1} 5 - (- \frac{3}{2} x + 4) d x

\frac{7}{4}

Decimal

1.75

Solution steps

\int_{0}^{1} 5 - (- \frac{3}{2} x + 4) d x

Simplify

= \int_{0}^{1} \frac{3}{2} x + 1 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_{0}^{1} \frac{3}{2} x d x + \int_{0}^{1} 1 d x

\int_{0}^{1} \frac{3}{2} x d x = \frac{3}{4}

\int_{0}^{1} 1 d x = 1

= \frac{3}{4} + 1

Simplify

\frac{3}{4} + 1 : \frac{7}{4}

= \frac{7}{4}

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What is the integral from 0 to 1 of 5-(-3/2 x+4) ?
The integral from 0 to 1 of 5-(-3/2 x+4) is 7/4