How do you find the integral of tanx from #[0,pi/4]# using the simpsons rule using 6 intervals?
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To find the integral of tan(x) from [0, π/4] using Simpson's Rule with 6 intervals, you can follow these steps:

Divide the interval [0, π/4] into 6 subintervals of equal width. Since there are 6 intervals, the width of each interval is (π/4)/6.

Compute the function values at the endpoints and midpoints of each subinterval. This will give you 7 function values in total.

Use Simpson's Rule formula: Integral ≈ (Δx/3) * [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + 2f(x4) + 4*f(x5) + f(x6)] Where Δx is the width of each subinterval, f(xi) represents the function value at each point, and the subscripts represent the indices of the points.

Substitute the values obtained in step 3 into the Simpson's Rule formula and perform the arithmetic to find the approximate value of the integral.
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To find the integral of tan(x) from 0 to π/4 using Simpson's rule with 6 intervals, follow these steps:
 Divide the interval [0, π/4] into 6 subintervals of equal width.
 Compute the function values at the endpoints and midpoints of each subinterval.
 Use Simpson's rule formula to approximate the integral over each pair of adjacent subintervals.
 Sum up the approximations for all subintervals to find the overall integral approximation.
The formula for Simpson's rule with equally spaced intervals is:
∫[a, b] f(x) dx ≈ (Δx / 3) * [f(a) + 4 * f(a + Δx) + f(a + 2Δx)]
Where Δx is the width of each subinterval, given by (b  a) / n, where n is the number of intervals.
Apply this formula to each pair of adjacent subintervals, starting from 0, and sum up the results to get the overall integral approximation.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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