Definite Integration Question 1
Question 1 - 24 January - Shift 1
The value of $12 \int_0^{3}|x^{2}-3 x+2| d x$ is
Show Answer
Answer: (22)
Solution:
Formula: Integration by substitution, Properties of definite integral, Modulus function, Standard Formula
$I= 12 \int_0^{3}|x^{2}-3 x+2| dx$
$I=12 \int_0^{3}|(x-\frac{3}{2})^{2}-\frac{1}{4}| d x$
subsitute $x-\frac{3}{2}=t \Rightarrow dx=dt$
$ I=24 \int_0^{3 / 2}|t^{2}-\frac{1}{4}| dt$
$ I =24[-\int_0^{1 / 2}(t^{2}-\frac{1}{4}) d t+\int _{1 / 2}^{3 / 2}(t^{2}-\frac{1}{4}) d t]=22$
