Write down the integral which gives the length of this

Question

Consider the curve x = t² , y = e^2t, 1 ≤ t ≤ 3.

a. Write down the integral which gives the length of this curve. Simplify the integrand, but do not calculate the integral.

b. In a city, the temperature (in ^oC) t hours after 9 am is approximately given by the function

T(t)= 10 + (70/9) sin Πt/12

Construct the integral which will compute the average temperature between 9 am and 9 pm. do not calculate the integral.