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}

f (x) = x^{2} (1 - 3 x)

e^{θ}

y = ln (1 + x)

\int \frac{48 x ^{2}}{( x - 18 ) ( x + 6 ) ^{2}} d x

\int - 2 sin (t) d t

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