Evaluate the integral. Check your answer by differentiating. (Remember the constant of integration.) √(16 8x + 21x6) dx
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- Please show all work ง 5. Evaluate the vector surface integral JJ (+2², x + 2y + 32², 5x − 2y + 2³) . Ndo. S Here, S is the sphere Sy²+2 1. = Since S is a closed surface, the outside of S is considered as the positive side on S. Hint: use the divergence theorem.Let f(x) = √√x, g(x) = x + 8 and h(x) = 5. (f + g)(16) X Compute the following function value.Let f be the function defined as, Ր f(x) = [* sin (t³) dt. Determine an expression for f(x) as a power series.
- Find at least the first four nonzero terms in a power series expansion about x = 0 for a general solution to the given differential equation. y'' +(x+6)y'+y=0 y(x) = ☐ + ... (Type an expression in terms of a and a₁ that includes all terms up to order 3.)Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the set whose sum is the zero vector. (Use S1, S2, and S3, respectively, for the vectors in the set.) (0, 0) = S={(5, 2), (-1, 1), (4, 0)) Express the vector s₁ in the set as a linear combination of the vectors $2 and $3. 51= Need Help? Read It Watch It Submit AnswerFind the derivative of the function f by using the rules of differentiation. 7 f(x) = -X417 4 f'(x) =
- A system is described by the action S[r, r'] = [ dt (x² + 4rª + mr³4), r(t) where m is a constant. Find the Euler-Lagrange equation for r = which extremises S. Interpret each of the terms that appear in the Euler- Lagrange equations in terms of Newton's second law. Find a conserved quantity for this system.answer should be bIn order to find a local minimum or maximum of a function, how do we manipulate the fırst derivative? Make it equal to zero O Make it positive O Make it negative Make it equal to f(x)