Evaluate the following intergal:-
integral of [Mvdv] with upper limit 'v' and lower limit 'u'
integration of M.v.dv with limits v and u
To evaluate the integral of [Mvdv] with upper limit 'v' and lower limit 'u', we can follow these steps:
1. Start by identifying the function that you are integrating. In this case, the function is Mv.
2. Determine the variable of integration. Here, the variable of integration is dv, which means we are integrating with respect to 'v'.
3. Apply the fundamental theorem of calculus, which states that if F(v) is an antiderivative of f(v), then the integral of f(v)dv from u to v is equal to F(v) evaluated at v minus F(v) evaluated at u.
4. Find an antiderivative F(v) of Mv. To do this, you need to determine a function F(v) such that the derivative of F(v) with respect to v is equal to Mv. This may involve some algebraic manipulation or knowledge of common antiderivatives.
5. Evaluate the antiderivative F(v) at the upper limit 'v' and lower limit 'u'. This will give you two values: F(v)|v and F(v)|u.
6. Subtract the value at the lower limit 'u' from the value at the upper limit 'v'. The result will be your final answer for the integral of Mvdv from u to v.
It is important to note that the specific form of M(v) will determine the steps necessary to find the antiderivative.