Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.)
2
1
6 ln(x)
1 + x
dx, n = 10
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
π/2
0
3
2 +
cos(x)
dx, n
= 4
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
4
0
ln(3 + ex) dx, n = 8
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
π/2
0
3
1 + cos(x)
dx, n = 4
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 5 2 cos(7x) x dx, n = 8
1 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's
Rule
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 2 0 e^x/ 1 + x^2 dx, n
= 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's
Rule
Use Simpson's Rule with n = 10 to approximate the area of the
surface obtained by rotating the curve about the x-axis. Compare
your answer with the value of the integral produced by your
calculator. (Round your answer to six decimal places.)
y = e^−x^2, 0 ≤ x ≤ 5
Use Simpson's Rule with n = 10 to approximate the area
of the surface obtained by rotating the curve about the
x-axis. Compare your answer with the value of the integral
produced by your calculator. (Round your answer to six decimal
places.)
y = x + sqrt x, 2 ≤ x ≤ 5
Use Simpson's Rule with n = 10 to approximate the area
of the surface obtained by rotating the curve about the
x-axis. Compare your answer with the value of the integral
produced by your calculator. (Round your answer to six decimal
places.)
y = x + sqrt x, 2 ≤ x ≤ 5