Evaluate the integral: the integral of the cube root of x, dx.
a. (3/4)x^(4/3)+C
b. (3/2)x^(2/3)+C
c. 1/(3x^(2/3))+C
d. None of these
I got (3x^(4/3)/4)+C. I was wondering if it would be D.
you have integral x^(1/3) dx
by the power rule, that is
(3/4) x^(4/3) + C
Choice A is correct.
In fact that is your answer, but you did not recognize it!
It's always sad to get a question wrong, but to miss it when you got it right is tragic.
Thanks, Steve. I was afraid that was the case.
Actually, your initial answer is correct. The integral of the cube root of x, ∛x dx, is indeed (3/4)x^(4/3) + C, where C represents the constant of integration. So the correct answer is option a.
Therefore, your answer of (3x^(4/3)/4) + C is correct. It is not option d.
To evaluate the integral of the cube root of x, we can use the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1), where n is any real number except for -1.
In this case, the function is the cube root of x, which can be written as x^(1/3). By using the power rule, we add 1 to the exponent and divide by the new exponent:
∫(x^(1/3)) dx = (x^(1/3+1))/(1/3+1) = (x^(4/3))/(4/3) = (3/4)x^(4/3) + C
Therefore, the correct answer is option a: (3/4)x^(4/3) + C.
So, your initial answer is correct. It is not option d: None of these.