Oh pardon me i meant to ask what is the anti-derivative of square root x
hint:
d/dx (x^1.5) = 1.5 x^0.5
Um I still don't get it because that hint was the derivative and I asked for the anti-derivative of square root x
To find the antiderivative of a function, in this case, the square root of x, you can use integration. The symbol for the antiderivative or integral of a function f(x) is ∫f(x) dx.
In this case, the antiderivative of √x, denoted as ∫√x dx, can be found using integration techniques.
Step 1: Rewrite the square root of x as a fractional exponent:
√x = x^(1/2)
Step 2: Apply the power rule of integration, which states that when integrating x^n, you add 1 to the exponent and divide by the new exponent:
∫x^n dx = (x^(n+1))/(n+1)
Applying the power rule to √x:
∫√x dx = ∫x^(1/2) dx
Using the power rule, add 1 to the exponent 1/2, to get:
(1/2 + 1) = 3/2
Step 3: Apply the power rule of integration:
∫x^(1/2) dx = (x^(3/2))/(3/2)
Simplifying further, you can invert the denominator and multiply:
∫x^(1/2) dx = (x^(3/2)) * (2/3)
So, the antiderivative of √x is:
∫√x dx = (2/3) * x^(3/2) + C
Where C is the constant of integration and can be any real number.