Explanation Given: ∫ cot 2 x csc 2 x d x Key Concept and Formula Used: Concept of substitution is used and formula used ∫ x n d x = x n + 1 n + 1 + C d d θ csc θ = − csc θ cot θ cot 2 θ = csc 2 θ − 1 Calculation: ∫ cot 2 x csc 2 x d x ................ (i) Let cot x = t Differentiate both side w.r.t to ‘x’ d d x cot x = d t d x − csc 2 x = d t d x (using d d θ cot θ = − csc 2 θ ) csc 2 x d x = − d t ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 8, Problem 31CRE

To determine

$\int \cot^{2} x \csc^{2} x d x$

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8, Problem 30CRE

Chapter 8, Problem 32CRE

Students have asked these similar questions

Graphically, explain the various forms of linear functions

2. Find the Bezier surface equation using the 9 control points shown below. Use the u and v directions shown. It is required to show all the calculation processes for finding Bernstein polynomials. Find the surface tangent, twist and normal vectors at point u=0.5 and v=0.5. (40 points) y 10 9 8 7 6 5 4 3 2 Poo и 1 1 2 3 4 5 6 7 8 9 10 10 X

A cable runs along the wall from C to P at a cost of $24 per meter, and straight from P to M at a cost of $26 per meter. If M is 10 meters from the nearest point A on the wall where P lies, and A is 72 meters from C, find the distance from C to P such that the cost of installing the cable is minimized and find this cost. C 72 P A 10 M

Chapter 8 Solutions

Calculus - Standalone book

Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

∫ cot 2 x csc 2 x d x

Solution Summary: The author explains the concept of substitution and the formula used.

Concept explainers

Videos

∫cot2xcsc2x dx

Want to see the full answer?

Chapter 8 Solutions

$\int \cot^{2} x \csc^{2} x d x$