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Popular Calculus >

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

Solution

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

Solution

- \frac{32}{3}

+1

Decimal

- 10.66666 \dots

Solution steps

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

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

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

= \frac{64}{3} - 32

Simplify

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

= - \frac{32}{3}

Graph

Popular Examples

integral from-pi to 0 of-2cos^2(x)sin(x)

\int_{- π}^{0} - 2 cos^{2} (x) sin (x) d x

integral from 0 to 10 of 25-(t-5)^2

\int_{0}^{10} 25 - (t - 5)^{2} d t

integral from 2 to 5 of (x^3-x^2+8)

\int_{2}^{5} (x^{3} - x^{2} + 8) d x

integral from 0 to 4 of-x^2-3x

\int_{0}^{4} - x^{2} - 3 x d x

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

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

Frequently Asked Questions (FAQ)

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