Question

9. \int \frac{x dx}{\sqrt{9 - x^2}} = \\ (a) \frac{1}{2}\sqrt{9 - x^2} + C \\ (b) \frac{1}{2}sin^{-1}(x/2) + C \\ (c) -2\sqrt{9 - x^2} + C \\ (d) -\sqrt{9 - x^2} + C \\ (e) None of the above.

          9. \int \frac{x dx}{\sqrt{9 - x^2}} = \\
(a) \frac{1}{2}\sqrt{9 - x^2} + C \\
(b) \frac{1}{2}sin^{-1}(x/2) + C \\
(c) -2\sqrt{9 - x^2} + C \\
(d) -\sqrt{9 - x^2} + C \\
(e) None of the above.
        
9. ∫(x dx)/(√(9 - x^2)) = 

(a) (1)/(2)√(9 - x^2) + C 

(b) (1)/(2)sin^-1(x/2) + C 

(c) -2√(9 - x^2) + C 

(d) -√(9 - x^2) + C 

(e) None of the above.

Added by Tiffany Q.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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int (xdx)/(sqrt(9-x^(2)))= (a) (1)/(2)sqrt(9-x^(2))+C (b) (1)/(2)sin^(-1)((x)/(2))+C (c) -2sqrt(9-x^(2))+C (d) -sqrt(9-x^(2))+C (e) None of the above. xdx aV9-x2+C (bsin-1x/2)+C c-29-x2+O d-9-x2+C (e) None of the above
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Transcript

-
00:01 In this problem we are given a function f of x equal to 5 times sine of x times cosine of x and we are given some choices.
00:13 Let's write them done and i will tell what the question is.
00:18 So a 5 sine x, cosine x b 2 .5 cosine x squared c 5 cosine x squared minus 5 sine x squared d 5 sine x squared plus 2 .5 x squared and e 2 .5 sine x squared okay the question is which of the following are anti -derivatives of this function namely which of the following are the integrals of this function so to confirm this to find out the solution it we can we will simply differentiate the given functions because antiderative means the integral so the derivative of this antiderivative is the function itself so let's do that for the first choice we have five times cosine x cosine x plus five times x minus sine x which is equal to 5 cosine x squared minus sine x squared this is equal to 5 times cosine 2 x the given function is 5 times sine x which can be written as 5 over 2 times 2 times sine x cosine x or sine 2 x clearly these are not equal so a cannot be true let's do the second choice let us different with it we get 2 .5 times 2 times cosine of x times minus sine of x which is equal to minus 5 sine of x cosine of x this is almost true but clearly not due to this minus sign so we don't accept b either okay let us to choice c upon differentiation we get the following five times 2 times cosine x minus sine x minus 5 times 2 times sine of x times cosine of x so we have minus 10 sine cos minus 10 sine cost minus 20 times sine of x times cosine of x clearly this is not true either due to this overall factor...
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