integral y^4/3 dx step by step?

Answer 1

Integral of y^4/3 dx:

The exponent of y is currently 4/3.
1. To integrate this term, add 1 to the exponent which is 4/3. You get 7/3.
2. Now you have y^7/3.
3. Divide the term in step 2 by the new exponent -- 7/3.
4. You'll get 3/7 * y^7/3. (Ans)

Answer 2

(assuming that the problem is y^4/3 dy)
General formula for the integral of (x^n) dx = [x^(n + 1)]/(n + 1)
in the gven problem
x = y ; dx = dy
n = 4/3
n + 1 = (4/3) + 1 = 7/3
so integral of (x^n) dx = x^(7/3)/(7/3) =
(3/7)[x^(7/3)]

(If the problem is y^4/3 dx)
the answer is y^4/3( x) , since y^4/3 is constant(k) with respect to x and integral of k dx = kx

Answer 3

∫ x ^ (n) dx = x ^ (n + 1) / (n + 1) + C
Thus:-
∫ x ^ (4/3) dx = x ^ (7/3) / (7/3) + C
∫ x ^ (4/3) dx = (3 / 7) x ^ (7/3) + C