Use the trapezoidal rule and Simpson's rule with n= 4, 8, ..., 512 to find approx- imate values of the area under the curve of y= f(x) for the following functions f(x) on the given intervals: (a) f(x)=e-², 0≤x≤ 10 (b) f(x)= tan-¹ (1+x²), 0 ≤x≤2 (c) f(x)=√xe², 0≤x≤1

Q: Find the area bounded by the curve y = x exp(-x²), the x-axis and the vertical line passing through…

A: Given: The given curve is, The x-axis and the vertical line passing through the maximum coordinate.…

Q: Estimate the area under the line y= 2x+1 using six rectangles and right endponits over the interval…

A:

Q: Find the area below the x-axis and bounded by the curve  y=1-2x for 5<=x<=7.

A: The given curve is: y = 1 - 2x;  where 5 &lt;= x &lt;= 7 The graph is as follows:

Q: Approximate the

A: Given,

Q: (a) curves y=, y =-x², lines x=1, x=2

A:

Q: f(x) = 3/x on the intend 0<x<4

A:

Q: What is the area under the curve for f(x) = 3x2 +5 between x=1 and x=10?

A:

Q: Estimate the area under the curve given by the function f(x)= ^3√x on the interval [1, 8] using 6…

A: The solution are next step