# Thread: integation limits

1. ## integation limits

find two numbers a and b with a<=b such that has the largest value

i have done the normal integration with expression coming in form of a,b what should i do after that

2. ## Re: integation limits

Originally Posted by prasum
find two numbers a and b with a<=b such that has the largest value

i have done the normal integration with expression coming in form of a,b what should i do after that
The function $f(x)=-x^2-x+6=-(x+3)(x-2)$ has zeros $x=-3 \quad x=2$

The function will only be above the $x-$axis on the set $(-3,2)$

3. ## Re: integation limits

Basically integrand has the largest value iff, it is positive in the interval. If you consider all interval where it is positive and integrate it, you will get the max value. Now, before becoming negative from positive, the polynomial changes sign, i.e, becomes zero. So, you have to find the roots, and integrate between the roots, between which it stays positive.

This is sufficient for quadratic polynomial. For others, you need to consider multiple intervals, and the integrand value on intermediate negative intervals also, and try to do an optimization.

Salahuddin
Maths online