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Popular >

integral from 0 to 4 of 5x-x^2-x

Solution

\int_{0}^{4} 5 x - x^{2} - x d x

Solution

\frac{32}{3}

+1

Decimal

10.66666 \dots

Solution steps

\int_{0}^{4} 5 x - x^{2} - x d x

Simplify

= \int_{0}^{4} - 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_{0}^{4} x^{2} d x + \int_{0}^{4} 4 x d x

\int_{0}^{4} x^{2} d x = \frac{64}{3}

\int_{0}^{4} 4 x d x = 32

= - \frac{64}{3} + 32

Simplify

- \frac{64}{3} + 32 : \frac{32}{3}

= \frac{32}{3}

Graph

Popular Examples

(\partial)/(\partial x)(ln(5+x^2y^2))

\frac{\partial}{\partial x} (ln (5 + x^{2} y^{2}))

integral of 3sqrt(x)+1/(sqrt(x))-1/x

\int 3 x + \frac{1}{x} - \frac{1}{x} d x

integral of 1/(xsqrt(x^2-25))

\int \frac{1}{x x ^{2} - 25} d x

limit as h approaches 0 of (3^h-1)/h

h \to 0 lim (\frac{3 ^{h} - 1}{h})

tangent of f(x)= 1/(sqrt(x)),\at x=25 tangent of

f (x) = \frac{1}{x}, at x = 25

Frequently Asked Questions (FAQ)

What is the integral from 0 to 4 of 5x-x^2-x ?
The integral from 0 to 4 of 5x-x^2-x is 32/3