What is $f (x) = \int x^{2} - 3 x - 2 d x$ $f(x) = int x^2-3x-2 dx$ if $f (- 1) = 2$ $f(-1) = 2$ ?

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What is $f (x) = \int x^{2} - 3 x - 2 d x$ $f(x) = int x^2-3x-2 dx$ if $f (- 1) = 2$ $f(-1) = 2$ ?

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Answer 1 · 2017-12-20T07:42:33

$f (x) = \frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 x + \frac{11}{6}$ $f(x) = x^3/3 - (3 x^2) / 2 - 2x + 11/6$

Explanation:

Let's first solve the integral:

$\int x^{2} - 3 x - 2 d x = \int x^{2} d x - 3 \int x d x - 2 \int 1 d x = \frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 x + C$ $int x^2 - 3x - 2 dx = int x^2 dx - 3 int x dx - 2 int 1 dx = x^3/3 - (3 x^2) / 2 - 2x + C$

We know that $f (- 1) = 2$ $f(-1) = 2$ . Therefore, we set $x = - 1$ $x = -1$ and solve the following equation:

$- \frac{1}{3} - \frac{3}{2} + 2 + C = 2$ $- 1/3 -3/2 + 2 + C = 2$ .

Solving this, we find that $C = \frac{11}{6}$ $C = 11/6$ , and thus

$f (x) = \frac{x^{3}}{3} - \frac{3 x^{2}}{2} - 2 x + \frac{11}{6}$ $f(x) = x^3/3 - (3 x^2) / 2 - 2x + 11/6$ .

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What is $f (x) = \int x^{2} - 3 x - 2 d x$ $f(x) = int x^2-3x-2 dx$ if $f (- 1) = 2$ $f(-1) = 2$ ?

1 Answer

Explanation:

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What is $f (x) = \int x^{2} - 3 x - 2 d x$ $f(x) = int x^2-3x-2 dx$ if $f (- 1) = 2$ $f(-1) = 2$ ?