What is the integral from-3 to 1 of x^2+2x-3 ?

The integral from-3 to 1 of x^2+2x-3 is -32/3

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integral from-3 to 1 of x^2+2x-3

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

- \frac{32}{3}

Decimal

- 10.66666 \dots

Solution steps

\int_{- 3}^{1} x^{2} + 2 x - 3 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_{- 3}^{1} x^{2} d x + \int_{- 3}^{1} 2 x d x - \int_{- 3}^{1} 3 d x

\int_{- 3}^{1} x^{2} d x = \frac{28}{3}

\int_{- 3}^{1} 2 x d x = - 8

\int_{- 3}^{1} 3 d x = 12

= \frac{28}{3} - 8 - 12

Simplify

\frac{28}{3} - 8 - 12 : - \frac{32}{3}

= - \frac{32}{3}

\frac{d y}{d x} + y^{7} x + 2 y = 0

\int - \frac{10}{x ^{2} + 16} d x

\int f (u) d u

f (x) = \frac{5 x}{x - 2}, (3, 15)

- y^{^{''}} + 36 y = 0

What is the integral from-3 to 1 of x^2+2x-3 ?
The integral from-3 to 1 of x^2+2x-3 is -32/3