What is $$\int_1^3 {\left| {1 - {x^4}} \right|} \,dx$$ equal to ?

Read the following information carefully and answer the questions given below.

Consider the functions f(x) = xg(x) and g(x) = $$\left[ {{1 \over x}} \right]$$, where [ . ] is the greatest integer function.

What is $$\int_{1/3}^{1/2} {g(x)\,dx} $$ equal to ?

Read the following information carefully and answer the questions given below.

Consider the functions f(x) = xg(x) and g(x) = $$\left[ {{1 \over x}} \right]$$, where [ . ] is the greatest integer function.

What is $$\int_{1/3}^1 {f(x)} \,dx$$ equal to ?

Read the following information carefully and answer the questions given below.

Given that, $${a_n} = \int_0^\pi {{{{{\sin }^2}\{ (n + 1)x\} } \over {\sin 2x}}dx} $$

Consider the following statements

1. The sequence $$\{ {a_{2n}}\} $$ is in AP with common difference zero.

2. The sequence $$\{ {a_{2n + 1}}\} $$ is in AP with common difference zero.

Which of the above statements is/are correct?