Detailed Explanations for Calculus 2 Equations

Sketch the signed area represented by the integral. Indicate the regions of positive and negative area.
$\int_{π}^{2 π} \sin x d x$

ffortunyu 2021-12-05

Use the Special Integration Formulas to find the indefinite integral.
$\int \sqrt{5 x^{2} - 1} d x$

jeliceg2 2021-12-04

Find the arc length of the curve on the given interval. Parametric Equations
$x = \sqrt{t}, y = 3 t - 1$ Interval $0 \leq t \leq 1$

impresijuzj 2021-12-04

Find two different sets of parametric equations for
$y = x^{2} + 6$

jippie771h 2021-12-04

Working with vector-valued functions For each vector-valuedfunction r, carry out the following steps.
a. Evaluate $lim_{t \Rightarrow 0} r (t) and lim_{t \Rightarrow \infty} r (t)$ , if each exists.
b. Find $r^{'} (t)$ and evaluate $r^{'} (0)$ .
c. Find $r t)$ .
d. Evaluate $\int r (t) d t .$
$r (t) = ⟨ t + 1, t^{2} - 3 ⟩$

Jason Watson 2021-12-04

Use polar coordinates to find the volume of the given solid. Below the paraboloid $z = 18 - 2 x^{2} - 2 y^{2}$ and above the xy-plane

ahgan3j 2021-12-04

Find $\frac{d y}{d x}$ and $\frac{d^{2} y}{{d x}^{2}}$ and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations
$x = 2 + \sec θ, y = 1 + 2 \tan θ$ Parameter $θ = \frac{- π}{3}$

varaderiyw 2021-12-04

A particle moves linearly from the point $(- 2, 4)$ to $(10, 0)$ in 4 seconds. Find parametric equations to describe this motion.

ostric16 2021-12-04

Find parametric equations for an object that moves along the ellipse
$\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1$
with the motion described.
The motion begins at $(2, 0)$ , is clokwise, and requires 2 seconds for a complete revolution.

Mahagnazk 2021-12-04

Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations
$P (0, 0, 0), Q (5, 2, 2)$

crapthach24 2021-12-04

Derivatives of vector-valued functions
Differentiate the following function
$r (t) = \tan t i + \sec t j + \cos^{2} t k$

Weltideepq 2021-12-04

Find parametric equation of the line passing through point $(4, 2)$ parallel to vector
$\vec{v} = - \hat{i} + 5 \hat{j}$

prelimaf1 2021-12-04

Let C be the curve described by the parametric equations $x (t) = t, y (t) = t^{3}$ .
a) sketch a graph of C.
b) find the vector-valued function f(t) associated with this parameterization of the curve C.
c) find the velocity vector and the speed of f(t) at t=1.

pamangking8 2021-12-04

Find the domain of the vector-valued function $r (t) = F (t) + G (t)$ , where
$F (t) = \cos t i - \sin t j + \sqrt{t} k$ , $G (t) = \cos t i + \sin t j$

Edmund Conti 2021-12-04

Represent the line segment from Pto Qby a vector-valued function. (Pcorresponds to t= 0. Q corresponds to t=1.)
$P (- 7, - 3, - 1), Q (- 2, - 9, - 9)$

gamomaniea1 2021-12-04

Verify the Sum and Product Rules for derivatives of vector-valued functions.

Eichowa4 2021-12-04

Express each integral as a single integral.
$\int_{0}^{3} f (x) d x + \int_{3}^{7} f (x) d x$

folklorahhe 2021-12-04

Find the values of x for which the series coverges.(Enter your answer using interval notation.)
$\sum_{η = 0}^{\infty} \frac{{(x - 1)}^{η}}{2^{η}}$
Find the sum of the series fot those values of x.

Maggenifh 2021-12-04

Critical Values: $z 0.005 = 2.575, z 0.01 = 2.325, z 0.025 = 1.96, z 0.05 = 1.645, z 0.1 = 1.282$
When $d . f . = 31 : t 0.005 = 2.744, t 0.01 = 2.453, t 0.025 = 2.040, t 0.05 = 1.696 t 0.1 = 1.309$
774 men from the New Model Army, 226 from the New Model Army, and 226 from the Royalist Army were included in a random sample of the 774 soldiers who took part in the Battle of Preston. Use a 0.05 significance level to test the claim that fewer than one quarter of the soldiers were Royalist

vousetmoiec 2021-12-04

Represent the line segment from P to Q by a vector-valued function.
P(7, 0, 9), Q(6,-6, 7)
r(t)=?

When you are dealing with any Calculus 2 homework, it is vital to have a look at the various questions and answers that will help you see whether you are correct in your approach to finding solutions. Even if you are dealing with analytical aspects of Calculus 2, it will be helpful as you are looking at provided equations and learn how the answers relate to original questions and problems specified.

Do not be afraid to take a look at the basic integration and related application if Calculus 2 does not sound clear or start with the Calculus 1 first.

Calculus 2

Calculus 2 Equations: Expert Solutions and More