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Popular >

integral from 1 to 4 of-x^2+5x-4

Solution

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

Solution

\frac{9}{2}

+1

Solution steps

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

\int_{1}^{4} x^{2} d x = 21

\int_{1}^{4} 5 x d x = \frac{75}{2}

\int_{1}^{4} 4 d x = 12

= - 21 + \frac{75}{2} - 12

Simplify

- 21 + \frac{75}{2} - 12 : \frac{9}{2}

= \frac{9}{2}

Popular Examples

integral of e^{x-2x}

\int e^{x - 2 x} d x

limit as x approaches infinity of (x-1)*e^{1/(x-1)}

x \to \infty lim ((x - 1) \cdot e^{\frac{1}{x - 1}})

integral of \sqrt[10]{x}

limit as x approaches 1 of (2-2x)/(x-1)

x \to 1 lim (\frac{2 - 2 x}{x - 1})

integral of 1/(xsqrt(x^2+5))

\int \frac{1}{x x ^{2} + 5} d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 4 of-x^2+5x-4 ?
The integral from 1 to 4 of-x^2+5x-4 is 9/2