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How do you find the derivative for f(x) integral (1-t2)(1 plus t4) from sin2x to 1?
Wiki User
∙ 5y ago
My suggestion is to multiply the binomials and do the integration directly, and then differentiate the result with respect to x.
(If that doesn't work, feel free to send me a picture of the problem and I'll give it another try.)
Wiki User
∙ 5y ago
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How do you integrate functions?
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
Why does you put plus c after integration?
When you find an indefinite integral of a function (ie, the integral of a function without integration limits) you are actually finding the antiderivative of that function. In other words, you are finding the function whose derivative is the function 'inside' the integral sign. Recall that the derivative of a constant is zero. The point here is that you add the 'c' to acknowledge the fact that when the derivative of the result of your integration effort is taken to get the original function it could, or would, have been followed by some unknown constant value that disappeared upon differentiation. That constant is denoted by the 'c'.
Formulae in derivative?
You will find several formulae in the Wikipedia article on "derivative".
What is the purpose of finding derivative?
The purpose of finding a derivative is to find the instantaneous rate of change. In addition, taking the derivative is used in integration by parts.
Find the derivative of 2x2?
2 x 2 = 4. 4 is a constant. The derivative of a constant is always 0. Therefore, The derivative of 2 x 2 is zero.
How do you integrate functions?
To integrate a function you find what the function you have is the derivative of. for example the derivative of x^2 is 2x. so the integral of 2x is x^2.
What is an integral that equals 2012 and for all the smart people out there can you give it as a formula?
For the integral to equal 2012, we need the derivative of 2012. Because this is zero, we could assume that there are no values that would give you 2012. However, if you integrate 0, you get a constant, and therefore, because we can choose this constant to be whatever we require, the integral of 0 could possibly equal 2012. However, if you are (more likely) required to find the integral of 2012, its 2012x, or the derivative of 2012 is as mentioned earlier, 0
How do you do integration math?
Well if you are talking about calculus, integration is the anti-derivative. So as my teacher explained to us, instead of going down, you will go up. For example if you have the F(x) = 2x, the F'(x) = 2. F'(x) is the derivative here, so you will do the anti of a derivative. So with the same F(x) = 2x the integral, is SF(x) = 1/3x^3. The Integral will find you the area under the curve.
Why does you put c after integration?
When you find an indefinite integral of a function (ie, the integral of a function without integration limits) you are actually finding the antiderivative of that function. In other words, you are finding the function whose derivative is the function 'inside' the integral sign. Recall that the derivative of a constant is zero. The point here is that you add the 'c' to acknowledge the fact that when the derivative of the result of your integration effort is taken to get the original function it could, or would, have been followed by some unknown constant value that disappeared upon differentiation. That constant is denoted by the 'c'.
Why does you put plus c after integration?
When you find an indefinite integral of a function (ie, the integral of a function without integration limits) you are actually finding the antiderivative of that function. In other words, you are finding the function whose derivative is the function 'inside' the integral sign. Recall that the derivative of a constant is zero. The point here is that you add the 'c' to acknowledge the fact that when the derivative of the result of your integration effort is taken to get the original function it could, or would, have been followed by some unknown constant value that disappeared upon differentiation. That constant is denoted by the 'c'.
How do you find sin theta when tan theta equals one fourth?
I will note x instead of theta tan(x) = sin(x) / cos(x) = 1/4 sin(x) = cos(x)/4 = ±sqrt(1-sin2x)/4 as cos2x + sin2 x = 1 4 sin(x) = ±sqrt(1-sin2x) 16 sin2x = 1-sin2x 17 sin2x = 1 sin2x = 1/17 sin(x) = ±1/sqrt(17)
How integration is reverse process of differentiation?
For example, the derivate of x2 is 2x; then, an antiderivative of 2x is x2. That is to say, you need to find a function whose derivative is the given function. The antiderivative is also known as the indifinite integral. If you can find an antiderivative for a function, it is fairly easy to find the area under the curve of the original function - i.e., the definite integral.
Integral of sin x sin 2x?
Ok, I know that sin 2x can be substituted out for 2 sin x cos x. so now I have the Integral of (sin x ) ( 2 sin x cos x ) dx which is 2 sin2x cos x dx If I use integration by parts with the u and dv, I find myself right back again..can you help. The book gives an answer, but I am not sure how it was achieved. the book gives 2/3 sin 2x cos x - 1/3 cos 2x sin x + C I may be making this more difficult than it is ? when you get the integral of 2 sin2x cos x dx use u substitution. u= sinx du= cosxdx. Then you'll get the integral of 2u^2 du.. .and then integrate...
What is the anti-derivitive?
The inverse operation to the derivative. Also called the integral. If you're given the derivative of a function, you can find the function again by performing the antiderivative. Many answers will be possible, all differing by a single number, so you normally add a general constant to the end. Example : The derivative of 6x^2 is 12x. The antiderivative of 12x is 6x^2 + any number.
Formulae in derivative?
You will find several formulae in the Wikipedia article on "derivative".
Which is the antiderivative of sinxcosx?
Using u-substitution (where u = sinx), you'll find the antiderivative to be 0.5*sin2x + C.
What does the derivative at a point mean?
The derivative at any point in a curve is equal to the slope of the line tangent to the curve at that point. Doing it in terms of the actual expression of the curve, find the derivative of the curve, then plug the x-value of the point into the derivative to find the derivative at that point.
