How do I find the antiderivative of (2pi y^4)/4?

Question

I know the anti-derivative of y^4 is y^5/5 but how do I perform this for ( 2 pi y^4/4)?

Answer 1

2pi is a constant therefore...

the Integral of 2piy^4/4 is

(pi*y^5)/10

Answer 2

(2piy^4)/4

the equation you are looking for can be expressed as

[x(pi)(y^5)]/z taking the first derivative of this ==>

5(x)pi(y^4)/z should be equal to 2(pi)(y^4)/4

[5(x)(pi)(y^4)]/z = [2(pi)(y^4)]/4  simplify the right side

[5(x)(pi)(y^4)]/z = [(pi)(y^4)]/2 divide both sides by pi and y^4 ==>

[5(x)]/z = 1/2 simplify 10x = z ==> if x = 1 z = 10 replace in the equation

[x(pi)(y^5)]/z ==> (1)(pi)(y^5)/10 ==>

pi(y^5)/10 the answer

the first derivative is 5(pi)(y^4)/10 = pi(y^4)/2 multiply the top and bottom by 2 ==> (2piy^4)/4 the value you were given.