Find the most general antiderivative of the function. Use C for the constant of the antiderivative.

Question

Find the most general antiderivative of the function.  Use C for the constant of the antiderivative.

anonymous · Answer

$$f(x)=9\sqrt{x}+4\cos x$$

dumbcow · Answer

sqrt x = x^1/2
use power rule to find anti derivative
$$\int\limits x^{n} = \frac{x^{n+1}}{n+1}$$

antiderivative of cos x is sin x

anonymous · Answer

im getting 6^3/2 -sinx

anonymous · Answer

does this sound correct?

dumbcow · Answer

first part is...but you dropped the 4 with the sin x
$$\int\limits 4\cos x = 4\sin x$$

anonymous · Answer

got it  so it would be 6^3/2-4sinx   that makes sense

dumbcow · Answer

why is it minus 4sin x ?

anonymous · Answer

for some reason i thought the antideriv of cos was (-sin)   is is positive sin right?

dumbcow · Answer

f(x)    --->   f'(x)
sin               cos
cos            -sin

so antiderivative of cos is positive sin

anonymous · Answer

thank you very much for your time and effort

dumbcow · Answer

yw