Consider the following argument on improper integrals. Suppose ∫ b a f(x)dx is a type 2 improper integral. To evaluate the integral, we evaluate its indefinite version F(x) = ∫ f(x)dx and apply FTC. Therefore, ∫ b a f(x)dx = F(b) - F(a). Select one: a. The argument does not contain any error. b. The argument contains at least one error.
Suppose f(x) is a continuous function and ∫ n+1 n f(x)dx = 0 for every integer n ≥ 0. Is it true that ∫ ∞ 0 f(x)dx = 0 ? True False
Find constants A, B for which -1 + t t 2 - 2t - 3 = A f + B g , where f, g are linear polynomials with leading coefficient 1 such that fg = t 2 - 2t - 3. Enter your answer in the form A * x + B * y or B * x + A * y and put brackets around fractions. For example, if A = 0 and B = 1/5, then enter 0 * x + (1/5) * y or (1/5) * x + 0 * y.
Given x = 3 2 sin(θ), express tan(θ) in terms of x and simplify as much as possible. Select one: a. tan(θ) = √ x 4 9 -x2 b. tan(θ) = √ x x2- 4 9 c. tan(θ) = √ x 9 4 +x2 d. tan(θ) = √ x x2- 9 4 e. tan(θ) = √ x 4 9 +x2 f. tan(θ) = √ x 9 4 -x2
Is it possible to evaluate ∫ cos(x)sin(x)dx without using the substitution rule? True False
Let R be the finite region bounded by curves y = 1/x and 3x + 3y = 10. A solid S is obtained by rotating the region R about the y-axis. Which of the following integral represents the volume of S ? Select one: a. π ∫ 3 1/3 1/x2 - 10-3x 3 2 dx b. π ∫ 3 1/3 1/y2 - 10-3y 3 2 dy c. π ∫ 3 1/3 10-3y 3 2 - 1/y2dy d. π ∫ 3 1/3 10-3x 3 2 - 1/x2 dx