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Popular >

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

Solution

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

Solution

\frac{20}{3}

+1

Decimal Notation

6.66666 \dots

Solution steps

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

\int_{1}^{5} x^{2} d x = \frac{124}{3}

\int_{1}^{5} 4 x d x = 48

= - \frac{124}{3} + 48

Simplify

- \frac{124}{3} + 48 : \frac{20}{3}

= \frac{20}{3}

Popular Examples

integral from 0 to 1 of x/(sqrt(x(1-x)))

\int_{0}^{1} \frac{x}{x ( 1 - x )} d x

integral from 1 to 3 of (x^2+x+4)

\int_{1}^{3} (x^{2} + x + 4) d x

integral from 1 to 9 of 3x^2+xsqrt(x)+1

\int_{1}^{9} 3 x^{2} + x x + 1 d x

integral from 0 to 1 of (x(x^2-1)^3)

\int_{0}^{1} (x (x^{2} - 1)^{3}) d x

integral from 0 to 6 of (180x-4x^2)

\int_{0}^{6} (180 x - 4 x^{2}) d x

Frequently Asked Questions (FAQ)

What is the integral from 1 to 5 of-x^2+4x ?
The integral from 1 to 5 of-x^2+4x is 20/3