Question

How do you evaluate the definite integral `int sinx dx` from `[0, pi/2]`?

Answer 1

I tried this:

Explanation:

First you solve the indefinite integral trying to find the Primitive (or anti-derivative) of your integrand; this is a function that DERIVED will give you `sin(x)`:

`intsin(x)dx=-cos(x)`

this is because if you derive `-cos(x)` you'll get exactly `sin(x)`!!!

After that we use the Fundamental Theorem of Calculus where, basically, we take our Primitive, we stick in first our upper extreme `pi/2` then the lower one `0` and subtract the values we obtain:

`-cos(pi/2)-(-cos(0))=1`

so we get:

`int_0^(pi/2)sin(x)dx=1`