The equation\\ $-?\frac{x^2}{u^2} - \sin(5u) = -2$\\ implicitly defines $u$ as a function of $x$.\\ Find $\frac{du}{dx}$\\ $\frac{du}{dx} = $\\Show your work and explain, in your own words, how you arrived at your answer.
Added by Juan Jos- P.
Close
Step 1
Step 1: Rewrite the equation sin(5u) = -2 2n as sin(5u) = -2. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 87 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integral and check your answer by differentiating. $$ \int\left[\phi+\frac{2}{\sin ^{2} \phi}\right] d \phi $$
INTEGRATION
The Indefinite Integral
g) ∫ ln(∑x+1)/2(x+∑x) dx 2. Evaluate the definite integrals: a) ∫[0 to π/2] cos x ⋅ sin(sin x) dx b) ∫[1 to 2] (e^(1/x)+4)/2x^2 dx
Adi S.
Suppose that you want to re-write an integral using a substitution, in this case, ∫ sin x / cos x dx = ∫ -1/u du. Determine the correct substitution that will accomplish this. That is, find u as a function of x that allows you to re-write the integral as shown above. The function u(x) we want is u=cos(x), in which case the differential of u is du=-sin(x) dx. Note: answer should be in the form u = f(x) and du = f'(x)dx. Part 2. Evaluate the indefinite integral above in terms of u. ∫ -1/u du = ln|-cos(u)|+C Note: answer should be in terms of u only.
William S.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD