Detailed Explanations for Calculus 2 Equations

Find the integral of the given definite integral.
$\int_{- 2}^{2} \frac{d x}{x + 2}$

Travis Fogle 2021-12-04

Evaluate the integral.
$\int (2 x^{3} - 3 x^{2}) d x$

pro4ph5e4q2 2021-12-04

Use a table of integrals to find the indefinite integral $\int \frac{e^{3 x}}{{(1 + e^{x})}^{3}} d x$

villane0 2021-12-04

Use a table of integrals to evaluate the following indefinite integrals. Some of the integrals require preliminary work, such as completing the square or changing variables, before they can be found in a table.
$\int \frac{d x}{\sqrt{9 x^{2} - 100}}, x > \frac{10}{3}$

actever6a 2021-12-03

What is meant by a specified integral?

kolonelyf4 2021-12-03

Evaluate the integral.
$\int \frac{(1 - \sin x)}{\tan x} d x$

rescuedbyhimw0 2021-12-03

Evaluate the following integrals:
$\int x^{2} \tan^{- 1} x d x$

embaseclielenzn 2021-12-03

Solve the definite/improper integral, tell if it converges or diverges.
$\int_{- 2}^{5} \frac{2 x + 4}{2 x^{2} + 21 x + 34} d x$

sklicatias 2021-12-03

Evaluate the iterated integral.
$\int_{- 1}^{1} \int_{0}^{π} x^{2} \sin y d y d x$

Lloyd Allen 2021-12-03

Evaluate iterated integral.
$\int_{0}^{3} \int_{1}^{2} (x y^{3} - x) d y d x$

Pearl Carney 2021-12-03

For the Vector-Valued Function
$r (t) = - 2 t^{5} i - 6 t^{4} j$
Find $r^{'} (t) \times r^{″} (t)$

katelineliseua 2021-12-03

Find a path that traces the circle in the plane $y = 5$ with radius $r = 2$ and center $(- 1, 5, - 5)$ with conctant speed 8.

$r_{1} (s) = ⟨ \underset{―}{} ⟩$

achieverh3 2021-12-03

Find parametric equations and symmetric equations for the line.
The line of intersection of the planes
$x + 2 y + 3 z = 1$
and
$x - y + z = 1$

Carolyn Moore 2021-12-03

Consider the helix represented by the vector-valued function $r (t) = ⟨ 2 \cos t, 2 \sin t, t ⟩$ .
(a) Write the length of the arc s on the helix as a function of t by evaluating the integral
(b) Solve for tin the relationship derived in part (a),and substitute the result into the original vector-valued function.This yields a parametrization of the curve interms of the arc length parameter s.
(c) Find the coordinates of the point on the helix for arc lengths $s = \sqrt{5}$ and $s = 4$ .
(d) Verify that $r^{'} (s) = 1 .$
$s = \int_{0}^{t} \sqrt{{[x^{'} (u)]}^{2} + {[y^{'} (u)]}^{2} + {[z^{'} (u)]}^{2} d u}$ .

Susan Munoz 2021-12-03

Find two different sets of parametric equations for the rectangular equation
$y = 4 x + 1, t = - 1$
at the point
$(- 2, - 7)$

ukelangf0 2021-12-03

Find parametric equations and a parameter interval for the motion of a particle that starts at the point $(- 2, 0)$ in the xy-plane and traces the circle $x^{2} + y^{2} = 4$ three times clokwise.

snijelihd 2021-12-03

Find the domain of the vector-valued function. (Enter your answer using interval notation.)
$r (t) = s q r (9 - t^{2}) i + t^{2} j - 5 t k$

Paganellash 2021-12-03

Trigonometric integrals. Evaluate the following integrals.
$\int_{0}^{π} {(1 - \cos 2 x)}^{\frac{3}{2}} d x$

Edmund Conti 2021-12-03

Use a table of integrals to evaluate the following integrals.
$\int_{0}^{\frac{π}{2}} \frac{d θ}{1 + \sin 2 θ}$

puntgewelb5 2021-12-03

Explain the differences between an indefinite integral and a definite integral.

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