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Integral Calculus

For $f (t) = (\frac{\cos t}{2}, \sin^{2} t)$ what is the distance between $f (\frac{π}{4})$ and $f (π)$ ?

Alannah Short 2022-06-14

The error bound formulas for trapezoidal rule and simpson's rule say that:
Error Bound for the Trapezoid Rule: Suppose that $\begin{array}{l} Error Bound for the Trapezoid Rule: Suppose that | f^{''} (x) | \leq k for some k \in R where \\ a \leq x \leq b . Then \\ | E_{T} | \leq k \frac{(b - a)^{3}}{12 n^{2}} \\ Error Bound for Simpson's Rule: Suppose that | f^{(4)} (x) | \leq k for some k \in R where \\ a \leq x \leq b . Then \\ | E_{S} | \leq k \frac{(b - a)^{5}}{180 n^{4}} \end{array}$
Using these formulas, is it possible to find functions where Trapezoid Rule is more accurate than Simpson's rule?

gvaldytist 2022-06-14

How do you write a vector equation and a parametric equation for each line: the line through $A (3, 0, 4)$ and parallel to the x-axis?

gnatopoditw 2022-06-14

How do I integrate $\frac{x^{2}}{\sqrt{9 x^{2} + 15}}$ ?

Alannah Short 2022-06-14

How do you find the equations of tangent lines at the point where the curve crosses itself $x = t^{2} - t$ and $y = t^{3} - 3 t - 1$ ?

Ezekiel Yoder 2022-06-13

Prove: Let $S (n)$ and $T (n)$ be the approximations of a function using n intervals by using Simpson's rule and the Trapezoid rule respectfully.
$S (2 n) = \frac{4 T (2 n) - T (n)}{3}$

telegrafyx 2022-06-13

Parametric function
${\begin{cases} x (t) = \sin^{2} t \\ y (t) = \cot^{2} t \end{cases}$
I need to explore this function, but I can't find enough information in my language. I don't know the steps of exploring the parametric function and building the graphic. I'd like to learn how to explore such a function in parametric form.

Hailie Blevins 2022-06-13

What is the polar form of $(8, 3)$ ?

boloman0z 2022-06-13

From a proof of Simpson's rule using Taylor polynomial where $f \in [x_{0}, x_{2}]$ and, for
$x_{1} = x_{0} + h$
where
$h = \frac{x_{2} - x_{0}}{2}$
it got:
$\int_{x_{0}}^{x_{2}} f (x) d x ≅ 2 h f (x_{1}) + h^{3} \frac{f^{″} (x_{1})}{3} + h^{5} \frac{f^{(4)} (ξ)}{60}$
and then, it changed $f^{″} (x_{1})$ by
$\frac{f (x_{0}) - 2 f (x_{1}) + f (x_{2})}{h^{2}}$
Where it came?

Roland Manning 2022-06-13

How do you rewrite the two parametric equations’ as one Cartesian equation $x = \sec (t), y = \tan (t), - \frac{π}{2} < t < \frac{π}{2} ?$

Kapalci 2022-06-13

Solve $\int_{0}^{\infty} \frac{1}{(x^{2} + b^{2})^{4}} d x$

oleifere45 2022-06-13

I am revising the modified euler method and would appreciate some help with this question:
The equation is
$y^{'} = \frac{2}{x} y + x^{2} e^{x}, y (1) = 0$
Use modified euler method to calculate $y (1.1)$ taking $h = 0.1$ (working to 4 decimal places)
Where do i start?

misurrosne 2022-06-13

How to solve $\int_{- 4}^{4} x^{2} \sqrt{16 - x^{2}} d x$ with beta function

Santino Bautista 2022-06-13

Parametric function differentiation problem
$x = a \cos g (t) and y = b \sin g (t)$
$x y^{2} \frac{d^{2} y}{d x^{2}} = b^{2} \frac{d y}{d x}$

meghaijemimah 2022-06-12

Evaluate the following definite integral using the fundamental theorem of calculus.

Evaluate the following definite integral using the fundamental theorem of calculus. 3 ∫ (z^2+2)/z dz 1

shmilybaby4i 2022-06-12

How do I find the 2 slopes at which this parametric function crosses itself?
$x (t) = 2 \sin (2 t) y (t) = 8 \sin (t)$

Jasmin Pineda 2022-06-12

$\frac{(b - a)^{5} f^{(4)} (c)}{2880 n^{4}}$
for a $c \in [a, b]$ , if the function has a continuous fourth derivative.
Is this for any $c$ in the interval, or just a unique one?

Sattelhofsk 2022-06-12

What is the distance between the following polar coordinates?:
$(3, \frac{7 π}{4}), (5, \frac{13 π}{8})$

Dale Tate 2022-06-11

How do you find parametric equations for the path of a particle that moves around the given circle $x^{2} + {(y - 2)}^{2} = 4$ clockwise, starting at (2, 2)?

Ezekiel Yoder 2022-06-11

What is the distance between the following polar coordinates?:
$(11, \frac{17 π}{12}), (4, \frac{π}{8})$

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Integral Calculus

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