### Estimation of battery charging from definite integral

Brief note on definite integrals Definite integrals are used to find the area under the given limits ‘a’ and ‘b’ for a differential derivative function. Though many rules are there to determine definite integrals for every specific function, basic algebraic function is given. For example, if ‘y’ as a function of ‘x’ or f(x) is given as, where ‘a’ is lower limit, ‘b’ is upper limit and n ≠ –1. Find the definite integral between the limits 1 to 4 for the function: y = 2x 2 + 3x. On solving this, the value is 64.5. Now applying this concept to charging a battery... a battery is charged under constant voltage by varying the current (C) in Amperes. The current passed with reference to time (t) in hours is governed by the equation, C = 0.5t 2 + 0.5t. Estimate the charge (Ah) given from 2.5 hours to 4.5 hours. (1 Ah is One Ampere given in one hour.) The problem is represented by the following figure shown below. This figure shows the curre