6. Find the value of each definite integral. (a) 6a +5 dar 6. Find the value of each definite integral. (a) 6a +5 dar
Find the exact value of the definite integral. 25 VI
QUESTION 5 The integral I= % dar +4 is to be approximated numerically. (a) Find the least integer M and the appropriate step size h so that the global error for the composite (10) Trapezoidal rule, given by As"(), a<<<0, 12 is less than 10-5 for the approximation of I. (b) Use the two-term Gaussian quadrature formula and 6 decimal place arithmetic to approximate I. (Hint: Parameters are c = 1, i = 1,2; = 0.5773502692, r2 = -0.5773502692) (9)...
Evaluate the definite integral. 5 S (5x2 - 6x +6)dx 0
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.
5. Find a definite integral (in terms of t) for the mass of a wire that lies along the curve r(t) = ti + "j + 2tk, 0 st 31, if the density is 8 = y. (Do not evaluate.)
1. Calculate the definite integral 1 (229-33 +5) de (a) Find an antiderivative F(x)= (b) Evaluate F(2) F(2) = (c) Evaluate F(1) F(1) = (d) Calculate the definite integral 3x + 5) dx = 2. Calculate the definite integral. Give exact answers. Зе -Te du (a) Find an antiderivative F(*) = (b) Evaluate F(0) F(0) (c) Evaluate F(-1) F(-1) = (d) Calculate the definite integral.
Find a definite integral that represents the arc length. r = 5 sec(θ) on the interval 0 ≤ θ ≤ π/3 (_______ )dθ
Differentiate the function f(x) = $* V t2 + +5 dt Find the definite integral (4 sint – 2 cos t)dt Find the indefinite integral. / (tan an x – 3)' sec? x dx
Use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral for the given value of n. Round your answer to four decimal places and compare the results with the exact value of the definite integral. foxt dx, n = 4 (x + 2)2 Trapezoidal Simpson's exact The velocity function, in feet per second, is given for a particle moving along a straight line. v(t) = 2 - t - 132, 1sts 13 (a) Find the...
x-5 dx. ) Evaluate the definite integral S 22-3x+2 Determine whether the improper integral S, dx converges. If convergent, find its value.