What values of a and b maximize the value of ſ(4x-x2) dx? (Hint: Where is the...
b What values of a and b maximize the value of ( ( 6x-x²) dx? a (Hint: Where is the integrand positive?) a= and b= maximize the given integral. (Simplify your answer. Type a whole number.)
1.) Find the definite integrals a.) sdx b.) S dx x2-4x+9 c.) ſ 4arccos xdx d.) Se-3x sin 5xdx e.) S In(4 + x2)dx f.) s cosst dt sin t g.) St tan 5 2xsec 4 2xdx h.) ſ sin(-4x)cos3xdx
2. a) Find an approximation to the integral (%(x2 - 4x) dx using a Riemann sum with right endpoints and n=4. b-a and x,-a +Ax. Use this to b) Using the definition ()dx = lim Žf(x7)Ar, where Ar = ? evaluate 1, (x2 - 4x) dx
No 13 and 14
(a) Find an approximation to the integral [** (x2 - 4x) dx using a Riemann sum with night endpoints and n = 8. Rg (b) iffis integrable on [a, b], then Serum f(x) dx lim 10 Fx) Ax, where Ax Als and Ax. Use this to evaluate 4x) dx
Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y...
Evaluate the function at the given values of the independent variable and simplify. f(x) = 4x -- (a) f(2) (b) f(-2) (c) f( - x) (a) f(2)= * (Type an integer or a fraction. Simplify your answer.) (b) f(-2)= 3 (Type an integer or a fraction Simplify your answer) (c) f(-x) = 4x+, 1 (Simplify your answer)
This Test: 18 pts possible 5 of 18 (1 comnplete) the foillowing vector field and region. Check for agreement Evaluate both integrals of the Divergence Theorem D= (xy.z): x2 + y2 + 22 s9) F (4x,3y,32); the Divergence Theorem. Select the correct choice below and fill in any answer boxes within your choice. Set up the volume integral OA !!! dp do d8, where the integrand does not simplity to a constant 0 0 O B. The integral simplifies to...
Maximize Q = xy, where x and y are positive numbers such that x +9y2 = 12 Write the objective function in terms of y. (Type an expression using y as the variable.) The interval of interest of the objective function is (Simplify your answer. Type your answer in interval notation.) . The maximum value of Q is (Simplify your answer.)
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)+...
(b) For any real number a > 0, O COS X dx = te /a. x2 + a? - [Hint: This is the real part of the integral obtained by replacing cos x by eix]