Preparing for my exams, I stumbled upon this particular problem.

I tried to calculate it using following formulae: $$ E = \int_{-\infty}^{\infty}|t|^2dt $$

Dividing it into two cases becasue of the absolute value of t, I got: $$ E = -\int_{-\infty}^{0}t²dt + \int_{0}^{\infty}t²dt $$

As result for the previous integral I get $ -\infty + \infty $ which in an indeterminate form.

Then I tried using the formula:

$$ E = \lim_{T\to\infty} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

, which yields $$\lim_{T\to\infty}(-\frac{T³}{24}+\frac{T³}{24})=0$$

Using that, I tried to calculate the power: $$ P = \lim_{T\to\infty} \frac{1}{T} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

Solving the integral once again it simplifies to: $$ \lim_{T\to\infty} \frac{1}{T}\cdot 0 = 0 $$

I'm having doubts whether my solution is correct, could you point me into the right direciton?

Preparing for my exams, I stumbled upon this particular problem.

I tried to calculate it using following formulae: $$ E = \int_{-\infty}^{\infty}|t|^2dt $$

Dividing it into two cases because of the absolute value of $t$, I got: $$ E = -\int_{-\infty}^{0}t²dt + \int_{0}^{\infty}t²dt $$

As result for the previous integral I get $ -\infty + \infty $ which in an indeterminate form.

Then I tried using the formula:

$$ E = \lim_{T\to\infty} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

which yields $$\lim_{T\to\infty}(-\frac{T³}{24}+\frac{T³}{24})=0$$

Using that, I tried to calculate the power: $$ P = \lim_{T\to\infty} \frac{1}{T} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

Solving the integral once again it simplifies to: $$ \lim_{T\to\infty} \frac{1}{T}\cdot 0 = 0 $$

I'm having doubts whether my solution is correct, could you point me into the right direction?

Preparing for my exams, I stumbled upon this particular problem.

I tried to calculate it using following formulae: $$ E = \int_{-\infty}^{\infty}|t|^2dt $$

Dividing it into two cases becasue of the absolute value of t, I got: $$ E = -\int_{-\infty}^{0}t²dt + \int_{0}^{\infty}t²dt $$

As result for the previous integral I get $ -\infty + \infty $ which in an indeterminate form.

Then I tried using the formula:

$$ E = \lim_{T\to\infty} \(-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt\) $$

, which yields $$\lim_{T\to\infty}\(-\frac{T³}{24}+\frac{T³}{24}\)=0$$

Using that, I tried to calculate the power: $$ P = \lim_{T\to\infty} \frac{1}{T} \(-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt\) $$

Solving the integral once again it simplifies to: $$ \lim_{T\to\infty} \frac{1}{T}\cdot 0 = 0 $$

I'm having doubts whether my solution is correct, could you point me into the right direciton?

Preparing for my exams, I stumbled upon this particular problem.

I tried to calculate it using following formulae: $$ E = \int_{-\infty}^{\infty}|t|^2dt $$

Dividing it into two cases becasue of the absolute value of t, I got: $$ E = -\int_{-\infty}^{0}t²dt + \int_{0}^{\infty}t²dt $$

As result for the previous integral I get $ -\infty + \infty $ which in an indeterminate form.

Then I tried using the formula:

$$ E = \lim_{T\to\infty} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

, which yields $$\lim_{T\to\infty}(-\frac{T³}{24}+\frac{T³}{24})=0$$

Using that, I tried to calculate the power: $$ P = \lim_{T\to\infty} \frac{1}{T} (-\int_{-\frac{T}{2}}^{0}t²dt + \int_{0}^{\frac{T}{2}}t²dt) $$

Solving the integral once again it simplifies to: $$ \lim_{T\to\infty} \frac{1}{T}\cdot 0 = 0 $$

I'm having doubts whether my solution is correct, could you point me into the right direciton?