Integration

Question

Answer 1

value of integral in (1,2) is zero. that means interval (1,x) and (x,2) having area with different sign..

atleast one crossing.
atleast one real root..

Comments

Why it would have atleast 1 crossing ..?can you please explain in little more detail..?

---

area under curve in (1,2) is 0..
that means der must be two (not exactly two it may be 1 or more than 2 alo) areas.. out of two, one is +ve and other is negative.. to get positive area graph should be above x axis and for negative area graph should  below x axis..

and function is multiplication of trigonometric and polynomial that is everywhere continuous.. so der must be an crossing to get two area of different sign..

in case of only one area with zero value is nothing but root of a equation.. i.e. 1 crossing..
more than two area gives more than 1 crossing..

---

number of crossings is number of real roots?