Question

How to find upper and lower bound of a definite integral given an unknown equation?

Answer 1

Finding the upper and lower bounds for a definite integral without an equation is pretty hard because how can we find the upper and lower bounds of definite integral if there is no equation given. But I will teach you how to find the lower and upper bounds of a definite integral, when the equation is like this


`\int\limits^6_1 t^(2) - 6t + 11dt`

So, i integrate this,

`( (t^(3) )/(3) - 3t^(2) + 11t) \int\limits^6_1`

I know I have a minimum at x=3 because;
f(t )= t^2 − 6t + 11
f′(t) = 2
t−6 = 0
2(t−3) = 0
t = 3
f(5) = 4
f(1) = −4