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

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

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

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

\frac{32}{3}

Decimal

10.66666 \dots

Solution steps

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

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

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

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

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

Simplify

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

= \frac{32}{3}

f^{^{'}} (x) = x (3 + 5 x), f (1) = 7

\int \frac{sin ( x )}{sin ( x ) + cos ( x )} d x

f, tan (f) (x) = 7 x^{4} + 4 \frac{x}{2} x^{3} + 1

\int (\frac{1}{x ^{3}} + \frac{7}{x ^{2}}) d x

f (x) = x^{2} + 5, (2, 9)

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