Question 1 (1 point) Determine the following definite integral 2 4x3 + 28x5 + 36 dx...
(1 point) Evaluate the definite integral. | << + 1)e+2+28-3 dx =
11. The graph of fis shown. Determine the value of f (x)dx= y = f(x) - X 16 32 48 64 1 12. Consider the definite integral s sin(tw) dw. What is the interval of integration for this integral? What is the variable of integration? What is the integrand? 13. Suppose that f* f(x) dx = 5, ſ. f(x)dx = -3, * g(x)dx = -1 and 1 g(x)dx = 7. Determine the value of each integral. Box Answer (5) $(x)+...
Use a change of variables to evaluate the following definite integral. 0 S xV81-x* dx -3 Determine a change of variables from x to u. Choose the correct answer below. O A. u=x4 O B. u = 81- x4 O C. u = 4x3 OD. u= 181 - x4 Write the integral in terms of u. S xV81-x* dx= du -3 Evaluate the integral. 0 5 x 181-x* dx= { -3 (Type an exact answer.)
Question 3. Evaluate the definite integral (show your steps!). T PV/2 e sin(x2) dx
Problem 10. (1 point) 5." -4 sin x dx a) Approximate the definite integral with the Trapezoid Rule and n = 4. b) Approximate the definite integral with Simpson's Rule and n = 4. c) Find the exact value of the integral.
(1 point) Call an improper definite integral type 1 if it is improper because the interval of integration is infinite. Call it type 2 if it is improper because the function takes on an infinite value within the interval of integration. Classify the type(s) for each of the following improper integrals. ? 1. sec(x) dx 0 ? 2. $x2-3x+6° x2 - 5x + 6 1 ? 3. Loints dx -00 x2 00 ? 4. dx
- Evaluate the definite integral. 1:22 4 dx (1) (2) 46 3 26 3 (3) 0 (4) 1
Express the limit as a definite integral. n lim Σ 1P10k1 TCK' AXk, where P is a partition of [6, 12] 6 OA. 7x6 dx 12 n B. 7x dx 1 12 Oc. zxdx de 12 OD | 42x2 dx Find the derivative. to y = = S cos Vt dt 0 O A. cos (x3) O B. sin (x3) OC. 6x5 OD. cos (x3) - 1 cos (x3) Solve the initial value problem. dy = x(2+x2)), y(0) = 0...
(1 point) The limit lim /2x + (x)?Ax 11 can be expressed as a definite integral on the interval [1, 8] of the form $(x) dx Determine a, b, and f(x). a = b= f(x) =
Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 1 2 3 dx 1 2 3 dx √1-x² (Type an exact answer.) S 11