So, my buddy is new to doing calculus and needs understanding this equation, it would be very appeciated for some

To evaluate the integral, rewrite the integrand as

Recall that

The leftmost sum is the well-known power series expansion for the function . In the rightmost sum, we just replace with .

This particular power series has a property called "uniform convergence". Roughly speaking, it's a property that says a sequence of functions converges to some limiting function in the sense that and get arbitrarily close to one another. If you have an idea of what "convergence" alone means, then you can think of "uniform convergence" as a more powerful form of convergence.

Long story short, this property allows us to interchange the order of summation/integration to write

The integral can be tackled with a substitution,

so that the integral is equivalent to

The remaining integral reduces to , which you can derive for yourself via integration by parts/power reduction.

So we have

which is the same as

and hence the identity.

answer: 10 turtles

step-by-step explanation: as turtles have four legs so 4.10=40 therefore birds are 4 which sue counted

look at photo