What is the integral of #sqrt(9-x^2)#? - Socratic
WEBDec 20, 2014 · arcsin(x 3) = u. Now we need to insert it into our solution: 9 2 arcsin(x 3) + 9 4 sin(2arcsin(x 3)) +C. This is the final solution. Answer link. Whenever I see these kind of functions, I recognize (by practicing a lot) that you should use a special substitution here: int sqrt (9-x^2)dx x = 3sin (u) This might look like a weird substitution ...
What is the domain and range of #f(x) = sqrt (9 - x^2)#? - Socratic
WEBAug 12, 2017 · Domain: [-3,3] Range: [0,3] The value under a square root cannot be negative, or else the solution is imaginary. So, we need 9-x^2\geq0, or 9\geqx^2, so x\leq3 and x\geq-3, or [-3.3]. As x takes on these values, we see that the smallest value of the range is 0, or when x=pm3 (so sqrt (9-9)=sqrt (0)=0), and a max when x=0, where …
How do you find the integral of sqrt(9-x^2)dx? - Socratic
WEBAug 17, 2015 · int sqrt(9-x^2)dx = 9/2(sin^(-1) (x/3) + x/3sqrt(1-(x/3)^2)) + C sin^2 A + cos^2 A = 1 cos 2A = 2cos^2 A - 1 sin 2A = 2sin Acos A Use substitution.
How do you integrate x^2/sqrt(9-x^2) dx? - Socratic
WEBJun 6, 2015 · I got 9/2arcsin(x/3) - x/2sqrt(9-x^2) + C. You can do this with trig substitution. Notice how this is of the form sqrt(a^2-x^2), which looks like sqrt(1 - sin^2theta), while sin^2theta + cos^2theta = 1. So, let: a = sqrt9 = 3 x = asintheta = 3sintheta dx = acosthetad theta = 3costhetad theta That gives sqrt(9 - x^2) = sqrt(3^2 - (3sintheta)^2) = sqrt9sqrt(1 …
How do you factor x^2-9? - Socratic
WEBMar 20, 2018 · (x-3)(x+3) >x^2-9" is a "color(blue)"difference of squares" "and in general factorises as" •color(white)(x)a^2-b^2=(a-b)(a+b) "here "a=x" and "b=3 rArrx^2-9=(x-3)(x+3)
How do you solve log_x 9 = -2? - Socratic
WEBMar 7, 2016 · Explanation: x−2 = 9. Make the exponent positive by using the rule x−n = 1 xn. 1 x2 = 9. 1 = 9x2. 1 9 = x2. √1 9 = x. 1 3 = x (a negative answer is not possible since the log of a negative number is undefined) Practice exercises:
What is the integral of sqrt(9-x^2)/x? - Socratic
WEBMar 30, 2018 · In general, when encountering an integral involving sqrt (a^2-x^2), make the trigonometric substitution x=asintheta. In this case, a^2=9, a=3, and so our substitution is x=3sintheta. Solving for dx yields dx=3costhetad theta. Apply the substitution: int (cancel3costhetasqrt (9-9sin^2theta))/ (cancel3sintheta)d theta Simplify: int (costhetasqrt ...
What is the antiderivative of #(9-x^2)^(1/2)#? - Socratic
WEBJul 10, 2018 · Explanation: Let x = 3sinθ ⇒ dx = 3cosθ dθ. ∴ ∫(9 − x2)1 2 dx. = ∫(9 −(3sinθ)2)1 2 (3cosθ dθ) = 3∫(3cosθ)cosθ dθ. = 9∫cos2θ dθ. = 9∫(1 + cos2θ 2) dθ. = 9 2 ∫(1 + cos2θ) dθ. = 9 2 (θ + 1 2 sin2θ) + C.
What is the domain and range of y =9 - x^2? - Socratic
WEBSep 8, 2017 · Explanation: y = 9 −x2 is an upside down parabola that has been shifted up 9 units. If it helps, you can rewrite the equation to make y = − x2 +9. The domain of any parabola is all real x, or x ∈ R. This does not change when shifting the parabola. The range of a normal parabola (y = x2) is y ≥ 0. The range of an upside-down parabola (y ...
How do you find the domain and range for #y =sqrt(9-x^2)
WEBFeb 18, 2016 · Domain: x in [-3,+3] Range: yin [0,3] I assume that we are dealing only with Real numbers. For Real numbers sqrt (a) is only defined if a>=0 rarr (9-x^2)>=0 rarr abs (x)<=3 which gives us the Domain. The maximum value of sqrt (9-x^2) occurs when x=0 and this maximum is sqrt (9) = 3 The minimum value of sqrt (9-x^2) occurs when x=+-3 …