- #1
ngkamsengpeter
- 195
- 0
Homework Statement
[tex]\int^{0}_{-\pi}\sqrt{1-cos^{2} x}[/tex]
Homework Equations
The Attempt at a Solution
I substitute into (sin x)^2 and get an answer of -2 but the answer should be 2 . how to i do this question.
just substitute (sin x)^2 and become sqr((sin x)^2) and then become sin x and substitute the limit from -pi to 0 get -2cristo said:How do you get an answer of -2? Perhaps you should show your work.
ngkamsengpeter said:just substitute (sin x)^2 and become sqr((sin x)^2) and then become sin x and substitute the limit from -pi to 0 get -2
cristo said:You need to integrate sin(x) before you plug in the limits.
cristo said:So you have [tex]\left[-\cos(x)\right]^0_{-\pi}=cos(0)-cos(-\pi)[/tex]. Can you evaluate that?[/QUOTE
[tex]\left[-\cos(x)\right]^0_{-\pi}=-cos(0)+cos(-\pi)[/tex]
shouldn't is be this way cristo.
Then , how to integrate [itex]|\sin(x)|[/itex]jpr0 said:maybe you should be interpreting [itex]\sqrt{\sin^2(x)}[/itex] as [itex]|\sin(x)|[/itex]
transgalactic said:but ((sin x)^2 )^0.5 gives us two answers
sinx and -sinx
?
sutupidmath said:yeah, generally it does, but look here we are only integrating in [-pi.0], and obviously sinx, where x is from [-pi,0] is always negative, so
I sin(x) I = -sinx, whenever x is from the interval [-pi. 0]
now as halls said, integrating this you will get the desired answer.
An integration problem is a mathematical problem that involves finding the integral of a function. This involves finding the area under the curve of the function, and is typically solved using calculus.
Solving integration problems is important because it allows us to find the total amount or accumulation of something, such as distance traveled, velocity, or volume. It is also used in many other fields such as physics, engineering, and economics.
There are several methods for solving integration problems, including substitution, integration by parts, trigonometric substitution, and partial fractions. Each method is useful for different types of functions and can make solving the problem more efficient.
Some common mistakes when solving integration problems include forgetting to include the constant of integration, using the wrong method, or making errors in algebraic manipulation. It is important to carefully check your work and practice regularly to avoid these mistakes.
Practice is key to improving your skills in solving integration problems. It is also helpful to understand the basic principles and rules of integration, as well as familiarizing yourself with various methods for solving different types of problems. Seeking help from a tutor or attending review sessions can also be beneficial.