Question

evaluate the integral.

$$ int _ { 6 } ^ { 6 } left( x ^ { 2 } - 3 x + 4 ight) ^ { 14 } d x $$

$$ int _ { 6 } ^ { 6 } left( x ^ { 2 } - 3 x + 4 ight) ^ { 14 } d x = square $$

(type an exact answer in simplified form.)

Explanation:

Step1: Recall the property of definite integrals

For a definite integral \(\int_{a}^{a}f(x)dx\), where \(a = 6\) and \(f(x)=(x^{2}-3x + 4)^{14}\).
The property of definite integrals states that \(\int_{a}^{a}f(x)dx=0\). This is because the interval of integration \([a,a]\) has a length of \(a - a=0\). Geometrically, the area between the curve \(y = f(x)\) and the \(x\) - axis over an interval of length \(0\) is \(0\).

Answer:

\(0\)