Indefinite Integration Questions

Use Stokes' Theorem to evaluate ∫ ∫S curlF.ds, where F(x, y, z) = (tan-¹(x²yz²), x²y, x² z²) and S is the cone x = √y² + z²,0 ≤ x ≤ 2, oriented in the direction of the positive x-axis. Hint: The

fire³z IPIE C

Evaluate the indefinite integral. √2²√1+z³dz

Evaluate the integral fz³ (zº – 10) dr by making the substitution u = = 6 - 10. I

Find √ ( = 1 + 2x + 6) de

∫1-tan²x1+tan²x dx

The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following function. The revenue from 115 gadgets is $37,271. -2/3 MR(x) = 4x (= 4x (x² +28,000) (a) Find the

Let f(x) = log3(x-4). a. Use transformations to graph the function. b. Write the domain and range in interval notation. c. Determine the vertical asymptote.

Solve the equation and enter its solution set below. If there is more than one solution, enter the solutions in solution set notation separated by a comma and in order from smallest to largest. If the

Evaluate the double integral for the function f(x, y) and the given region R. f(x, y) = y e^x^³; R is bounded by x =y/6, x = 1 and y = 0.

Evaluate the double integral for the function f(x, y) and the given region R. f(x, y) = 3y + 5x; R is the rectangle defined by 3 ≤ x ≤ 6 and 3 ≤ y ≤ 6

Find the domain of the function. (Enter your answers using interval notation.) h(x, y) = In(x + y - 4) The domain of h is the set of all ordered pairs (x, y) such that x E__, yE__, and (x + y)E__.