What is $f (x) = \int 3 x - 4 d x$ $f(x) = int 3x-4 dx$ if $f (2) = 2$ $f(2) = 2$ ?

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What is $f (x) = \int 3 x - 4 d x$ $f(x) = int 3x-4 dx$ if $f (2) = 2$ $f(2) = 2$ ?

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Answer 1 · 2016-02-12T09:47:38

$f (x) = \frac{3}{2} x^{2} - 4 x + 4$ $f(x) = 3/2 x^2 - 4x + 4$

Explanation:

using $\int a x^{n} d x = \frac{a x^{n + 1}}{n + 1} + c$ $int ax^n dx = (ax^(n+1))/(n+1) + c$

this is standard integral where c is the constant of integration

then $\int (3 x - 4) d x = \frac{3}{2} x^{2} - 4 x + c$ $int(3x - 4 ) dx = 3/2 x^2 - 4x + c$

f(2) = 2 , allows c , to be found

hence : $\frac{3}{2} .4 - 4 (2) + c = 2$ $3/2 .4 - 4(2) + c = 2$

6 - 8 + c = 2 → c = 4

$\Rightarrow \int (3 x - 4) d x = \frac{3}{2} x^{2} - 4 x + 4$ $rArr int(3x - 4)dx = 3/2 x^2 - 4x + 4$

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What is $f (x) = \int 3 x - 4 d x$ $f(x) = int 3x-4 dx$ if $f (2) = 2$ $f(2) = 2$ ?

1 Answer

Explanation:

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What is $f (x) = \int 3 x - 4 d x$ $f(x) = int 3x-4 dx$ if $f (2) = 2$ $f(2) = 2$ ?